NEET Physics Class 11 Chapter 7 Gravitation Multiple Choice Question Ans Answers

NEET Physics Class 11 Chapter 7 Gravitation Multiple Choice Question Ans Answers

Question 1. Weight of an object is :

1. Normal reaction between ground and the object
2. Gravitational force exerted by earth on the object.
3. Dependent on frame of reference.
4. Net force on the object

Answer: 2. Gravitational force exerted by earth on the object

Question 2. The weight of a body at the centre of the earth is –

1. Zero
2. Infinite
3. Same as on the surface of earth
4. None of the above

Answer: 1. Zero

Question 3. If the distance between two masses is doubled, the gravitational attraction between them.

1. Is doubled
2. Becomes four times
3. Is reduced to half
4. Is reduced to a quarter

Answer: 4. Is reduced to a quarter

Question 4. The gravitational force between two stones of mass 1 kg each separated by a distance of 1 metre in vacuum is –

1. Zero
2. 6.675 × 10^-5 Newton
3. 6.675 × 10^-11 Newton
4. 6.675 × 10^-8 Newton

Answer: 3. 6.675 × 10^-11 newton

Question 5. Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is –

1. \(\mathrm{v}=\frac{1}{2 R} \sqrt{\frac{1}{G m}}\)
2. \(\mathrm{v}=\sqrt{\frac{G m}{2 R}}\)
3. \(\mathrm{v}=\frac{1}{2} \sqrt{\frac{G m}{R}}\)
4. \(\mathrm{v}=\sqrt{\frac{4 G m}{R}}\)

Answer: 3. \(\mathrm{v}=\frac{1}{2} \sqrt{\frac{G m}{R}}\)

Question 6. Reason of weightlessness in a satellite is –

1. Zero gravity
2. Centre of mass
3. Zero reaction force by satellite surface
4. None

Answer: 3. Zero reaction force by satellite surface

Question 7. The gravitational force Fgbetween two objects does not depend on –

1. Sum of the masses
2. Product of the masses
3. Gravitational constant
4. Distance between the masses

Answer: 1. Sum of the masses

Question 8. A mass M splits into two parts m and (M – m), which are then separated by a certain distance. What ratio (m/M) maximies the gravitational force between the parts?

1. \(\frac{2}{3}\)
2. \(\frac{3}{4}\)
3. \(\frac{1}{2}\)
4. \(\frac{1}{3}\)

Answer: 3. \(\frac{1}{2}\)

Question 9. On a planet (whose size is the same as that of Earth and mass 4 times of the Earth) the energy needed to lift a 2kg mass vertically upwards through a 2m distance on the planet is (g = 10m/sec² on surface of earth)

1. 16 J
2. 32 J
3. 160 J
4. 320 J

Answer: 3. 160 J

Question 10. The dimensions of universal gravitational constant are :

1. [M^-1L³T^-2]
2. [ML²T^-1]
3. [M^-2L³T^-2]
4. [M^-2L²T^-1]

Answer: 1. [M^-1L³T^-2]

Question 11. If the change in the value of ‘g’ at a height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth) –

1. x = h
2. x = 2h
3. x = \(\frac{h}{2}\)
4. x = h²

Answer: 2. x = 2h

Question 12. The moon’s radius is 1/4 that of the Earth and its mass is 1/80 time that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

1. g/4
2. g/5
3. g/6
4. g/8

Answer: 2. g/5

Question 13. Assuming the earth to be a homogeneous sphere of radius R, its density in terms of G (constant of gravitation) and g (acceleration due to gravity on the surface of the earth) is

1. 3g/(4πRG)
2. 4πg/(3RG)
3. 4πRg/(3G)
4. 4πRG/(3g)

Answer: 1. 3g/(4πRG)

Question 14. An object is placed at a distance of R/2 from the centre of earth. Knowing mass is distributed uniformly, acceleration of that object due to gravity at that point is: (g = acceleration due to gravity on the surface of earth and R is the radius of earth)

1. g
2. 2 g
3. g/2
4. None of these

Answer: 3. g/2

Question 15. Altitude at which acceleration due to gravity decreases by 0.1% approximately : (Radius of earth = 6400 km)

1. 3.2 km
2. 6.4 km
3. 2.4 km
4. 1.6 km

Answer: 1. 3.2 km

Question 16. An iron ball and a wooden ball of the same radius are released from a height ‘h’ in vacuum. The time taken by both of them to reach the ground is –

1. Unequal
2. Exactly equal
3. Roughly equal
4. Zero

Answer: 2. Exactly equal

Question 17. The correct answer to above question is based on –

1. Acceleration due to gravity in vacuum is same irrespective of size and mass of the body
2. Acceleration due to gravity in v
3. acuum depends on the mass of the body
4. There is no acceleration due to gravity in vacuum
5. In vacuum there is resistance offered to the motion of the body and this resistance depends on the mass of the body

Answer: 1. Acceleration due to gravity in vacuum is same irrespective of size and mass of the body

Question 18. When a body is taken from the equator to the poles, its appearent weight –

1. Remains constant
2. Increases
3. Decreases
4. Increases at N-pole and decreases at S-pole

Answer: 2. Increases

Question 19. A body of mass m is taken to the bottom of a deep mine. Then –

1. Its mass increases
2. Its mass decreases
3. Its weight increases
4. Its weight decreases

Answer: 4. Its weight decreases

Question 20. As we go from the equator to the poles, the value of g

1. Remains the same
2. Decreases
3. Increases
4. Decreases upto a latitude of 45º

Answer: 3. Increases

Question 21. Force of gravity is least at

1. The equator
2. The poles
3. A point in between equator and any pole
4. None of these

Answer: 1. The equator

Question 22. Spot the wrong statement :

1. The acceleration due to gravity ‘g’ decreases if –
2. We go down from the surface of the earth towards its centre
3. We go up from the surface of the earth
4. We go from the equator towards the poles on the surface of the earth
5. The rotational velocity of the earth is increased

Answer: 3. We go from the equator towards the poles on the surface of the earth

Question 23. Choose the correct statement from the following : Weightlessness of an astronaut moving in a satellite is a situation of –

1. Zero g
2. No gravity
3. Zero mass
4. Free fall

Answer: 4. Free fall

Question 24. If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be –

1. g/2
2. 4g
3. g/4
4. 2g

Answer: 2. 4g

Question 25. The moon’s radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is –

1. g/4
2. g/5
3. g/6
4. g/8

Answer: 2. g/5

Question 26. The radius of the earth is around 6000 km. The weight of a body at a height of 6000 km from the earth’s surface becomes –

1. Half
2. One-fourth
3. One third
4. No change

Answer: 2. One-fourth

Question 27. At what height from the ground will the value of ‘g’ be the same as that in a 10 km deep mine below the surface of the earth –

1. 20 km
2. 10 km
3. 15 km
4. 5 km

Answer: 4. 5 km

Question 28. At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = Radius of earth)

1. 2R
2. R
3. 1.414 R
4. 0.414 R

Answer: 3. 1.414 R

Question 29. What will be the acceleration due to gravity at height h if h >> R. Where R is the radius of the earth and g is the acceleration due to gravity on the surface of the earth.

1. \(\frac{g}{\left(1+\frac{h}{R}\right)^2}\)
2. \(g\left(1-\frac{2 h}{R}\right)\)
3. \(\frac{g}{\left(1-\frac{h}{R}\right)^2}\)
4. \(g\left(1-\frac{h}{R}\right)\)

Answer: 1. \(\frac{g}{\left(1+\frac{h}{R}\right)^2}\)

Question 30. If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be (g = 9.8 m/s²)

1. 19.6 m/s²
2. 9.8 m/s²
3. 4.9 m/s²
4. 2.45 m/s²

Answer: 1. 19.6 m/s²

Question 31. The acceleration due to gravity at the pole and equator can be related as –

1. gp< ge
2. gp= ge= g
3. gp= ge< g
4. gp> ge

Answer: 4. gp> ge

Question 32. The depth at which the effective value of acceleration due to gravity is \(\frac{g}{4}\) is

1. R
2. \(\frac{3 R}{4}\)
3. \(\frac{R}{2}\)
4. \(\frac{R}{4}\)

Answer: 2. \(\frac{R}{2}\)

Question 33. Two bodies of mass 100 kg and 104 kg are lying one meter apart. At what distance from a 100 kg body will the intensity of the gravitational field be zero

1. \(\frac{1}{9} m\)
2. \(\frac{1}{10} m\)
3. \(\frac{1}{11} m\)
4. \(\frac{10}{11} \mathrm{~m}\)

Answer: 3. \(\frac{1}{11} m\)

Question 34. Figure shows a hemispherical shell having uniform mass density. The direction of gravitational field intensity at point P will be along:

1. a
2. b
3. c
4. d

Answer: 3. c

Question 35. Two bodies of mass 10² kg and 10³ kg are lying 1m apart. The gravitational potential at the mid-point of the line joining them is

1. 0
2. –1.47 Joule/kg
3. 1.47 Joule/kg
4. –1.47 × 10^-9 joule/kg

Answer: 4. –1.47 × 10^-9 joule/kg

Question 36. A simple pendulum has a period T₁ when on the earth’s surface, and T₂ when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T₂/T₁ is:

1. 1
2. \(\sqrt{2}\)
3. 4
4. 2

Answer: 4. 2

Question 37. Near earth time period of a satellite is 4 h. Find its time period at a distance 4R from the centre of earth:

1. 32 h
2. \(\left(\frac{1}{8^3 \sqrt{2}}\right) h\)
3. \(8^3 \sqrt{2} h\)
4. 16 h

Answer: 1. 32 h

Question 38. The radius of the orbit of a planet is two times that of the Earth. The time period of a planet is:

1. 4.2 T
2. 2.8 T
3. 5.6 T
4. 8.4 T

Answer: 2. 2.8 T

Question 39. In the case of earth:

1. The field is zero, both at the centre and infinity
2. The potential is zero, both at the centre and infinity
3. The potential is the same, both at centre and infinity but not zero
4. The potential is maximum at the centre

Answer: 1. Field is zero, both at the centre and infinity

Question 40. What would be the angular speed of the earth, so that bodies lying on the equator may appear weightless? (g = 10m/s² and radius of earth = 6400 km)

1. 1.25 × 10^-3 rad/sec
2. 1.25 × 10^-2 rad/sec
3. 1.25 × 10^-4 rad/sec
4. 1.25 × 10^-1 rad/sec

Answer: 1. 1.25 × 10^-3 rad/sec

Question 41. The speed with which the earth has to rotate on its axis so that a person on the equator would weigh (3/5)th as much as present will be (Take the equatorial radius as 6400 km.)

1. 3.28 × 10^-4 rad/sec
2. 7.826 × 10^-4 rad/sec
3. 3.28 × 10^-3 rad/sec
4. 7.28 × 10^-3 rad/sec

Answer: 2. 7.826 × 10^-4 rad/sec

Question 42. A body of mass m is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (g = gravity field at the surface of the earth)

1. mgR
2. \(\frac{3}{4} \mathrm{mgR}\)
3. \(\frac{1}{3} \mathrm{mgR}\)
4. \(\frac{2}{3} \mathrm{mgR}\)

Answer: 2. \(\frac{3}{4} \mathrm{mgR}\)

Question 43. The change in potential energy when a body of mass m is raised to a height n R from the earth’s surface is (R = Radius of earth)

1. mgR
2. nmgR
3. \(\mathrm{mgR} \frac{n^2}{n^2+1}\)
4. \(\mathrm{mgR} \frac{n}{n+1}\)

Answer: 4. \(\mathrm{mgR} \frac{n}{n+1}\)

Question 44. If the mass of the earth is M, the radius is R and the gravitational constant is G, then work done to take 1 kg mass from the earth’s surface to infinity will be –

1. \(\sqrt{\frac{G M}{2 R}}\)
2. \(\frac{G M}{R}\)
3. \(\sqrt{\frac{2 G M}{R}}\)
4. \(\frac{G M}{2 R}\)

Answer: 2. \(\frac{G M}{R}\)

Question 45. A rocket is launched with a velocity of 10 km/s. If the radius of the earth is R, then the maximum height attained by it will be

1. 2R
2. 3R
3. 4R
4. 5R

Answer: 3. 3R

Question 46. What is the intensity of the gravitational field at the centre of a spherical shell –

1. Gm/r²
2. g
3. Zero
4. None of these

Answer: 3. Zero

Question 47. The escape velocity of a body of 1 kg mass on a planet is 100 m/sec. The gravitational Potential energy of the body on the Planet is –

1. – 5000 J
2. – 1000 J
3. – 2400 J
4. 5000 J

Answer: 1. – 5000 J

Question 48. The kinetic energy needed to project a body of mass m from the earth’s surface (radius R) to infinity is –

1. mgR/2
2. 2 mgR
3. mgR
4. mgR/4

Answer: 3. mgR

Question 49. The escape velocity of a sphere of mass m from Earth having mass M and radius R is given by –

1. \(\sqrt{\frac{2 G M}{R}}\)
2. \(2 \sqrt{\frac{G M}{R}}\)
3. \(\sqrt{\frac{2 G M m}{R}}\)
4. \(\sqrt{\frac{G M}{R}}\)

Answer: 1. \(\sqrt{\frac{2 G M}{R}}\)

Question 50. If g is the acceleration due to gravity at the earth’s surface and r is the radius of the earth, the escape velocity for the body to escape out of the earth’s gravitational field is –

1. gr
2. \(\sqrt{2 g r}\)
3. g/r
4. r/g

Answer: 2. \(\sqrt{2 g r}\)

Question 51. For the moon to cease to remain the earth’s satellite, its orbital velocity has to increase by a factor of –

1. 2
2. \(\sqrt{2}\)
3. \(1 / \sqrt{2}\)
4. \(\sqrt{3}\)

Answer: 2. \(\sqrt{2}\)

Question 52. Escape velocity on a planet is ve. If the radius of the planet remains the same and the mass becomes 4 times, the escape velocity becomes –

1. 4v_e
2. 2v_e
3. v_e
4. v_e

Answer: 2. 2v_e

Question 53. How many times is the escape velocity (Ve), of orbital velocity (V0) for a satellite revolving near Earth –

1. \(\sqrt{2}\) times
2. 2 times
3. 3 times
4. 4 times

Answer: 1. \(\sqrt{2}\) times

Question 54. If the radius of a planet is R and its density is, the escape velocity from its surface will be –

1. \(v_e \propto R\)
2. \(\mathrm{v}_{\mathrm{e}} \propto \mathrm{R} \sqrt{p}\)
3. \(\mathrm{v}_{\mathrm{e}} \propto \frac{\sqrt{\rho}}{R}\)
4. \(\mathrm{v}_{\mathrm{e}} \propto \frac{1}{\sqrt{\rho R}}\)

Answer: 2. \(\mathrm{v}_{\mathrm{e}} \propto \mathrm{R} \sqrt{p}\)

Question 55. If V, R and g denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is –

1. \(v=\sqrt{g R}\)
2. \(V=\sqrt{\frac{4}{3} g R^3}\)
3. \(\mathrm{V}=\mathrm{R} \sqrt{g}\)
4. \(V=\sqrt{2 g R}\)

Answer: 4. \(V=\sqrt{2 g R}\)

Question 56. If the radius of a planet is four times that of Earth and the value of g is the same for both, the escape velocity on the planet will be –

1. 11.2 km/s
2. 5.6 km/s
3. 22.4 km/s
4. None

Answer: 3. 22.4 km/s

Question 57. If the radius and acceleration due to gravity both are doubled, the escape velocity of the earth will become.

1. 11.2 km/s
2. 22.4 km/s
3. 5.6 km/s
4. 44.8 km/s

Answer: 2. 22.4 km/s

Question 58. If g is the acceleration due to gravity on the earth’s surface, the gain in P.E. of an object of mass m raised from the surface of the earth to a height of the radius R of the earth is

1. mgR
2. 2mgR
3. 12mgR
4. 14mgR

Answer: 3. 12mgR

Question 59. A missile is launched with a velocity less than the escape velocity. The sum of kinetic energy and potential energy will be

1. Positive
2. Negative
3. Negative or positive, uncertain
4. Zero

Answer: 2. Negative

Question 60. If v_e is escape velocity and v₀ is the orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by :

1. \(\mathrm{v}_0=\sqrt{2} v_e\)
2. \(v_0=v_e\)
3. \(v_e=\sqrt{2 v_0}\)
4. \(v_e=\sqrt{2} v_0\)

Answer: 4. \(v_e=\sqrt{2} v_0\)

Question 61. An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0. Its potential energy is :

1. − Eº
2. 1.5 Eº
3. 2 Eº
4. Eº

Answer: 3. 2 Eº

Question 62. The mass and radius of the earth and moon are M₁, R₁ and M₂, R₂ respectively. Their centres are d distance apart. With what velocity should a particle of mass m be projected from the midpoint of its centres so that it may escape out to infinity?

1. \(\sqrt{\frac{G\left(M_1+M_2\right)}{d}}\)
2. \(\sqrt{\frac{2 G\left(M_1+M_2\right)}{d}}\)
3. \(\sqrt{\frac{4 G\left(M_1+M_2\right)}{d}}\)
4. \(\sqrt{\frac{G M_1 M_2}{d}}\)

Answer: 3. \(\sqrt{\frac{4 G\left(M_1+M_2\right)}{d}}\)

Question 63. A satellite has to revolve around the earth in a circular orbit of radius 8 × 10³ km. The velocity of projection of the satellite in this orbit will be

1. 16 km/sec
2. 8 km/sec
3. 3 km/sec
4. 7.08 km/sec

Answer: 4. 7.08 km/sec

Question 64. The ratio of the radius of the earth to that of the moon is 10. The ratio of g an earth to the moon is 6. The ratio of the escape velocity from the Earth’s surface to that from the moon is approximately

1. 10
2. 8
3. 4
4. 2

Answer: 2. 8

Question 65. Acceleration due to gravity on a planet is 10 times the value on the Earth. Escape velocity for the planet and the earth are V_p and V_e respectively Assuming that the radii of the planet and the earth are the same, then

1. \(V_{\mathrm{P}}=10 \mathrm{~V}_{\mathrm{e}}\)
2. \(V_P=\sqrt{10} V_e\)
3. \(V_P=\frac{V_e}{\sqrt{10}}\)
4. \(V_P=\frac{V_e}{10}\)

Answer: 3. \(V_P=\frac{V_e}{\sqrt{10}}\)

Question 66. A space shuttle is launched in a circular orbit near the Earth’s surface. The additional velocity given to the space shuttle to get free from the influence of gravitational force will be

1. 1.52 km/s
2. 2.75 km/s
3. 3.28 km/s
4. 5.18 km/s

Answer: 3. 3.28 km/s

Question 67. A body of mass m is situated at a distance 4R_e above the earth’s surface, where R_e is the radius of the earth. How much minimum energy be given to the body so that it may escape

1. mgR_e
2. 2mgR_e
3. \(\frac{m g R_e}{5}\)
4. \(\frac{m g R_e}{16}\)

Answer: 3. \(\frac{m g R_e}{5}\)

Question 68. The potential energy of a body of mass 3kg on the surface of a planet is 54 joule. The escape velocity will be

1. 18m/s
2. 162 m/s
3. 36 m/s
4. 6 m/s

Answer: 4. 6 m/s

Question 69. The escape velocity from a planet is v₀. The escape velocity from a planet having twice the radius but the same density will be

1. 0.5 v₀
2. v₀
3. 2v₀
4. 4v₀

Answer: 3. 2v₀

Question 70. If the kinetic energy of a satellite orbiting around the earth is doubled then

1. The satellite will escape into space.
2. The satellite will fall down on the earth
3. The radius of its orbit will be doubled
4. The radius of its orbit will become half

Answer: 1. The satellite will escape into the space.

Question 71. The escape velocity from the earth does not depend upon

1. Mass of earth
2. Mass of the body
3. Radius of earth
4. Acceleration due to gravity

Answer: 2. Mass of the body

Question 72. There is no atmosphere on the moon because

1. It is near the earth
2. It is orbiting around the earth
3. There was no gas at all
4. The escape velocity of gas molecules is less than their root-mean-square velocity

Answer: 4. The escape velocity of gas molecules is less than their root-mean-square velocity

Question 73. The escape velocity is

1. 2gR
2. gR
3. \(\sqrt{g R}\)
4. \(\sqrt{2g R}\)

Answer: 4. \(\sqrt{2g R}\)

Question 74. A particle of mass m is taken through the gravitational field produced by a source S, from A to B, along the three paths as shown in the figure. If the work done along the paths 1, 2 and 3 is W₁, W₂ and W₃ respectively, then

1. W₁= W₂= W₃
2. W₂> W₃= W₂
3. W₃= W₂> W₁
4. W₁> W₂> W₃

Answer: 1. W₁= W₂= W₃

Question 75. The escape velocity of a particle of mass m varies as :

1. m²
2. m
3. m⁰
4. m^-1

Answer: 3. m⁰

Question 76. Acceleration due to gravity at the earth’s surface is g ms^-2. Find the effective value of gravity at a height of 32 km from sea level : (R_e= 6400 km) (R_e= 6400 km)

1. 0.5 g ms^-2
2. 0.99 g ms^-2
3. 1.01 g ms^-2
4. 0.90 g ms^-2

Answer: 2. 0.99 g ms^-2

Question 77. The radius of orbit of the satellite of earth is R. Its kinetic energy is proportional to :

1. \(\frac{1}{R}\)
2. \(\frac{1}{\sqrt{R}}\)
3. R
4. \(\frac{1}{R^{3 / 2}}\)

Answer: 1. \(\frac{1}{R}\)

Question 78. A cosmonaut is orbiting earth in a spacecraft at an altitude h = 630 km with a speed of 8 km/s. If the radius of the earth is 6400 km, the acceleration of the cosmonaut is

1. 9.10 m/s²
2. 9.80 m/s²
3. 10.0 m/s²
4. 9.88 m/s²

Answer: 1. 9.10 m/s²

Question 79. A very very large number of particles of the same mass m are kept at horizontal distances of 1m, 2m, 4m, 8m and so on from (0,0) point. The total gravitational potential at this point is (addition of G.P. of infinite terms = \(\frac{a}{1-r}\) where a = first term, r = common ratio) :

1. – 8G m
2. – 3G m
3. – 4G m
4. – 2G m

Answer: 4. – 2G m

Question 80. A body starts from rest at a point, distance R₀ from the centre of the earth of mass M, radius R. The velocity acquired by the body when it reaches the surface of the earth will be

1. \(\mathrm{GM}\left(\frac{1}{R}-\frac{1}{R_0}\right)\)
2. \(2 \mathrm{GM}\left(\frac{1}{R}-\frac{1}{R_0}\right)\)
3. \(\sqrt{2 G M\left(\frac{1}{R}-\frac{1}{R_0}\right)}\)
4. \(2 \mathrm{GM} \sqrt{\left(\frac{1}{R}-\frac{1}{R_0}\right)}\)

Answer: 3. \(\sqrt{2 G M\left(\frac{1}{R}-\frac{1}{R_0}\right)}\)

Question 81. The relation between the escape velocity from the earth and the velocity of a satellite orbiting near the earth’s surface is

1. v_e = 3v
2. v_e= v
3. v_e= 2v
4. v_e= v/2

Answer: 2. v_e= v

Question 82. A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is :

1. \(\sqrt{\frac{G M}{R}}\)
2. \(\sqrt{\frac{2 G M}{R}}\)
3. \(\sqrt{\frac{5}{4} \frac{G M}{R}}\)
4. \(\sqrt{\frac{3 G M}{R}}\)

Answer: 1. \(\sqrt{\frac{G M}{R}}\)

Question 83. A satellite of mass m is circulating around the earth with constant angular velocity. If the radius of the orbit is R₀ and the mass of the earth is M, the angular momentum about the centre of the earth is

1. \(M \sqrt{G M R_0}\)
2. \(M \sqrt{G m R_0}\)
3. \(M \sqrt{\frac{G M}{R_0}}\)
4. \(M \sqrt{\frac{G M}{R_0}}\)

Answer: 1. \(M \sqrt{G M R_0}\)

Question 84. Which of the following quantities is conserved for a satellite revolving around the earth in a particular orbit?

1. Angular velocity
2. Force
3. Angular momentum
4. Velocity

Answer: 3. Angular momentum

Question 85. The distance of Neptune and Saturn from sun are nearly 10¹³ and 10¹² meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio –

1. \(\sqrt{10}\)
2. 100
3. \(10 \sqrt{10}\)
4. \(1 / \sqrt{10}\)

Answer: 3. \(10 \sqrt{10}\)

Question 86. The period of a satellite in a circular orbit of radius R is T, and the period of another satellite in a circular orbit of radius 4R is –

1. 4T
2. T/4
3. 8T
4. T/8

Answer: 3. 8T

Question 87. If a body describes a circular motion under an inverse square field, the time taken to complete one revolution T is related to the radius of the circular orbit as –

1. T ∝ r
2. T ∝ r²
3. T² ∝ r³
4. T ∝ r⁴

Answer: 3. T² ∝ r³

Question 88. The escape velocity of a sphere of mass m from Earth having mass M and radius R is given by –

1. \(\sqrt{\frac{2 G M}{R}}\)
2. \(2 \sqrt{\frac{G M}{R}}\)
3. \(\sqrt{\frac{2 G M m}{R}}\)
4. \(\sqrt{\frac{G M}{R}}\)

Answer: 1. \(\sqrt{\frac{2 G M}{R}}\)

Question 89. The escape velocity from the earth is about 11 km/second. The escape velocity from a planet having twice the radius and the same mean density as the Earth is –

1. 22km/sec
2. 11 km/sec
3. 5.5 km/sec
4. 15.5 km/sec

Answer: 1. 22km/sec

Question 90. A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of the earth in the new orbit is 2 times that of the earlier orbit. The time period in the second orbit is –

1. 4.8 hours
2. \(48 \sqrt{2}\) hours
3. 24 hrs
4. Infinite

Answer: 2. \(48 \sqrt{2}\) hours

Question 91. Two satellites A and B go around planet P in circular orbits having radial 4R and R respectively. If the speed of the satellite A is 3V, the speed of the satellite B will be

1. 12 V
2. 6 V
3. 4/3 V
4. 3/2 V

Answer: 2. 6 V

Question 92. The escape velocity for a rocket from earth is 11.2 km/sec. Its value on a planet where the acceleration due to gravity is double that on the earth and the diameter of the planet is twice that of the earth will be in km/sec-

1. 11.2
2. 5.6
3. 22.4
4. 53.6

Answer: 3. 22.4

Question 93. A satellite revolves around the earth in an elliptical orbit. Its speed

1. Is the same at all points in the orbit
2. Is greatest when it is closest to the earth
3. Is greatest when it is farthest from the earth
4. Goes on increasing or decreasing continuously depending upon the mass of the satellite

Answer: 2. Is greatest when it is closest to the earth

Question 94. Time period of revolution of a satellite around a planet of radius R is T. The Period of revolution around another planet, whose radius is 3R but has the same density is –

1. \(\frac{T}{3 \sqrt{3}}\)
2. 3T
3. 9T
4. \(3 \sqrt{3} T\)

Answer: 1. \(\frac{T}{3 \sqrt{3}}\)

Question 95. If Veand V₀ represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R, then –

1. \(V_e=V_0\)
2. \(\sqrt{2} V_0=V_e\)
3. \(V_e=\frac{1}{\sqrt{2}} V_o\)
4. None of these

Answer: 2. \(\sqrt{2} V_0=V_e\)

Question 96. A spherical planet far out in space has a mass of M₀ and a diameter D₀. A particle will experience acceleration due to gravity which is equal to

1. GM₀/D_0²
2. 2mGM₀/D_0²
3. 4GM₀/D_0²
4. GmM₀/D_0²

Answer: 3.4GM₀/D_0²

Question 97. A satellite can be in a geostationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

1. \(\frac{r}{2}\)
2. \(\frac{r}{2 \sqrt{2}}\)
3. \(\frac{r}{(4)^{1 / 3}}\)
4. \(\frac{r}{(2)^{1 / 3}}\)

Answer: 3. \(\frac{r}{(4)^{1 / 3}}\)

Question 98. Consider a satellite going around the earth in an orbit. Which of the following statements is wrong –

1. It is a freely falling body
2. It suffers no acceleration
3. It is moving at a constant speed
4. Its angular momentum remains constant

Answer: 2. It suffers no acceleration

Question 99. The period of a satellite in a circular orbit around a planet is independent of –

1. The mass of the planet
2. The radius of the planet
3. The mass of the satellite
4. All the three parameters (1), (2) and (3)

Answer: 3. The mass of the satellite

Question 100. A small satellite is revolving near the earth’s surface. Its orbital velocity will be nearly.

1. 8 km/sec
2. 11.2 km/sec
3. 4 km/sec
4. 6 km/sec

Answer: 1. 8 km/sec

Question 101. A satellite revolves around the earth in an elliptical orbit. Its speed.

1. Is the same at all points in the orbit
2. Is greatest when it is closest to the earth
3. Is greatest when it is farthest from the earth
4. Goes on increasing or decreasing continuously depending upon the mass of the satellite

Answer: 2. Is greatest when it is closest to the earth

Question 102. If the height of a satellite from the earth is negligible in comparison to the radius of the earth R, the orbital velocity of the satellite is –

1. gR
2. gR/2
3. \(\sqrt{g / R}\)
4. \(\sqrt{g R}\)

Answer: 4. \(\sqrt{g R}\)

Question 103. Orbital velocity of an artificial satellite does not depend upon –

1. Mass of the earth
2. Mass of the satellite
3. Radius of the earth
4. Acceleration due to gravity

Answer: 2. Mass of the satellite

Question 104. The time period of a geostationary satellite is –

1. 24 hours
2. 12 hours
3. 365 days
4. One month

Answer: 1. 24 hours

Question 105. Which one of the following statements regarding artificial satellites of the earth is incorrect –

1. The orbital velocity depends on the mass of the satellite
2. A minimum velocity of 8 km/sec is required by a satellite to orbit quite close to the earth
3. The period of revolution is large if the radius of its orbit is large
4. The height of a geostationary satellite is about 36000 km from earth

Answer: 1. The orbital velocity depends on the mass of the satellite

Question 106. Two identical satellites are at R and 7R away from the earth’s surface, the wrong statement is (R = Radius of the earth)

1. The ratio of total energy will be 4
2. The ratio of kinetic energies will be 4
3. The ratio of potential energies will be 4
4. The ratio of total energy will be 4 but the ratio of potential and kinetic energies will be 2

Answer: 4. Ratio of total energy will be 4 but the ratio of potential and kinetic energies will be 2

Question 107. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60º with the vertical, then the escape velocity will be –

1. 11 km/s
2. \(11 \sqrt{3} \mathrm{~km} / \mathrm{s}\)
3. \(\frac{11}{\sqrt{3}} \mathrm{~km} / \mathrm{s}\)
4. 33 km/s

Answer: 1. 11 km/s

Question 108. The distance of a geo-stationary satellite from the centre of the earth (Radius R = 6400 km) is nearest to –

1. 5 R
2. 7 R
3. 10 R
4. 18 R

Answer: 2. 7 R

Question 109. Periodic time of a satellite revolving above Earth’s surface at a height equal to R, radius of Earth, is [g is acceleration due to gravity at Earth’s surface]

1. \(2 \pi \sqrt{\frac{2 R}{g}}\)
2. \(4 \sqrt{2} \pi \sqrt{\frac{R}{g}}\)
3. \(2 \pi \sqrt{\frac{R}{g}}\)
4. \(8 \pi \sqrt{\frac{R}{g}}\)

Answer: 2. \(4 \sqrt{2} \pi \sqrt{\frac{R}{g}}\)

Question 110. Given the radius of Earth ‘R’ and length of a day ‘T’ the height of a geostationary satellite is [G-Gravitational constant. M-Mass of Earth]

1. +R
2. – R
3. – R
4. None

Answer: 3. – R

Question 111. The distance of a geostationary satellite from the surface of the earth radius (Re= 6400 km) in terms of Re is –

1. 13.76 R_e
2. 10.76 R_e
3. 5.56 R_e
4. 2.56 R_e

Answer: 3. 5.56 R_e

Question 112. The orbital velocity of a planet revolving close to the earth’s surface is –

1. \(\sqrt{2 g R}\)
2. \(\sqrt{g R}\)
3. \(\sqrt{\frac{2 g}{R}}\)
4. \(\sqrt{\frac{g}{R}}\)

Answer: 2. \(\sqrt{g R}\)

Question 113. A satellite moves around the earth in a circular orbit of radius r with speed v. If the mass of the satellite is M, its total energy is –

1. \(-\frac{1}{2} \mathrm{Mv}^2\)
2. \(\frac{1}{2} M v^2\)
3. \(\frac{3}{2} M v^2\)
4. Mv²

Answer: 1. \(-\frac{1}{2} \mathrm{Mv}^2\)

Question 114. If a satellite is shifted towards the earth. The time period of the satellite will be –

1. Increase
2. Decrease
3. Unchanged
4. Nothing can be said

Answer: 2. Decrease

Question 115. Two satellites A and B go around a planet in circular orbits having radii 4R and R, respectively. If the speed of satellite A is 3v, then the speed of satellite B is –

1. \(\frac{3 v}{2}\)
2. \(\frac{4 v}{2}\)
3. 6v
4. 12v

Answer: 3. 6v

Question 116. If gravity field due to a point mass follows \(\mathrm{g} \propto \frac{1}{r^3}\) instead of \(\frac{1}{r^2}\), then the relation between time period of a satellite near earth’s surface and radius of its orbit r will be –

1. T² ∝ r³
2. T ∝ r²
3. T² ∝ r
4. T ∝ r

Answer: 2. T ∝ r²

Question 117. A satellite appears to be at rest when seen from the equator. Its height from the earth’s surface is nearly

1. 35800km
2. 358000 km
3. 6400km
4. Such a satellite cannot exist

Answer: 1. 35800km

Question 118. A body is dropped by a satellite in its geostationary orbit

1. It will burn on entering the atmosphere
2. It will remain in the same place with respect to the earth
3. It will reach the earth in 24 hours
4. It will perform uncertain motion

Answer: 2. It will remain in the same place with respect to the earth

Question 119. A satellite of Earth can move only in those orbits whose plane coincides with

1. The plane of a great circle of the earth
2. The plane passing through the poles of the earth
3. The plane of a circle at any latitude on earth
4. None of these

Answer: 1. The plane of a great circle of the earth

Question 120. A satellite launching station should be

1. Near the equatorial region
2. Near the polar region
3. On the polar axis
4. All locations are equally good

Answer: 1. Near the equatorial region

Question 121. The minimum number of satellites needed to be placed at the surface of the earth for worldwide communication between any two locations is –

1. 6
2. 4
3. 3
4. 5

Answer: 3. 3

Question 122. A geostationary satellite orbits around the earth in a circular orbit with a radius of 36000 km. Then, the time period of a spy satellite orbiting a few hundred kilometres above the earth’s surface (R_Earth = 6400 km) will approximately be :

1. 1/2 hr
2. 1 hr
3. 2 hr
4. 4 hr

Answer: 3. 2 hr

Question 123. A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

1. \(\frac{1}{2} m V^2\)
2. mV²
3. \(\frac{3}{2} m V^2\)
4. 2mV²

Answer: 2. mV²

Question 124. Two satellites of earth, S₁ and S₂ are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statements is true:

1. The time period of S₁ is four times that of S₂
2. The potential energies of the earth and satellite in the two cases are equal
3. S₁ and S₂ are moving at the same speed
4. The kinetic energies of the two satellites are equal

Answer: 3. S₁ and S₂ are moving at the same speed

Question 125. The orbital speed of a satellite revolving near the earth is :

1. \(\sqrt{2 g R}\)
2. \(\sqrt{g R}\)
3. \(\sqrt{g / R}\)
4. \(\sqrt{2 g / R}\)

Answer: 2. \(\sqrt{g R}\)

Question 126. If the radius of the earth is decreased by 1% and mass remains constant, then the acceleration due to gravity

1. Decrease by 2%
2. Decrease by 1%
3. Increase by 1%
4. Increase by 2%

Answer: 4. Increase by 2%

Question 127. The escape velocity for a rocket is 11.2 km/s. If it is taken to a planet where the radius and acceleration due to gravity are double that of earth, then the escape velocity will be :

1. 5.6 m/s
2. 11.2 m/s
3. 22.4 km/s
4. 44.2 m/s

Answer: 3. 22.4 km/s

Question 128. Suppose the radius of the moon’s orbit around the earth is doubled. Its period around the earth will become:

1. 1/2 times
2. \(\sqrt{2}\) times
3. 22/3 times
4. 23/2 times

Answer: 4. 23/2 times

Question 129. In the case of an orbiting satellite if the radius of the orbit is decreased :

1. Its Kinetic Energy decreases
2. Its Potential Energy increase
3. Its Mechanical Energy decreases
4. Its speed decreases

Answer: 3. Its Mechanical Energy decreases

Question 130. A satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will

1. Continue to move with velocity v along the original orbit
2. Move with a velocity v, tangentially to the original orbit
3. Fall down with increasing velocity
4. Ultimately come to rest somewhere in the original orbit

Answer: 2. Move with a velocity v, tangentially to the original orbit

Question 131. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period becomes

1. 10 hour
2. 80 hour
3. 40 hour
4. 20 hour

Answer: 3. 40 hour

Question 132. The escape velocity for a body projected vertically upwards from the surface of the earth is 11 km/s. If the body is projected at an angle of 45º with the vertical, the escape velocity will be :

1. \(11 \sqrt{2} \mathrm{~km} / \mathrm{s}\)
2. 22 km/s
3. 11 km/s
4. \(11 / \sqrt{2} \mathrm{~m} / \mathrm{s}\) m/s

Answer: 3. 11 km/s

Question 133. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is :

1. gx
2. \(\frac{g R}{R-x}\)
3. \(\frac{g R^2}{R+x}\)
4. \(\left(\frac{g R^2}{R+x}\right)^{1 / 2}\)

Answer: 4. \(\frac{g R}{R-x}\)

Question 134. The time period of an earth satellite in a circular orbit is independent of :

1. The mass of the satellite
2. The radius of its orbit
3. Both the mass and radius of the orbit
4. Neither the mass of the satellite nor the radius of its orbit

Answer: 1. The mass of the satellite

Question 135. If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is :

1. 2mgR
2. \(\frac{1}{2} m g R\)
3. \(\frac{1}{4} m g R\)
4. mgR

Answer: 2. \(\frac{1}{2} m g R\)

Question 136. The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of the earth. When both ‘d’ and ‘h’ are much smaller than the radius of the earth, then, which one of the following is correct?

1. \(\mathrm{d}=\frac{h}{2}\)
2. \(\mathrm{d}=\frac{3 h}{2}\)
3. d = 2h
4. d = h

Answer: 3. d = 2h

Question 137. A particle of mass 10 kg is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G = 6.67 × 10^-11 Nm²/kg²);

1. 13.34 × 10^-10 J
2. 3.33 × 10^-10 J
3. 6.67 × 10^-9 J
4. 6.67 × 10^-7 J

Answer: 4. 6.67 × 10^-7 J

Question 138. If g_E and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio

1. 1
2. 0
3. g_E/g_M
4. g_M/g_E

Answer: 1. 1

Question 139. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s^-1, the escape velocity from the surface of the planet would be

1. 11 km s^-1
2. 110 km s^-1
3. 0.11 km s^-1
4. 1.1 km s^-1

Answer: 2. 110 km s^-1

Question 140. The distance of neptune and saturn from the sun is nearly 10¹³ and 10¹² meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio –

1. \(\sqrt{10}\)
2. 100
3. 10
4. 1/10

Answer: 3. 10

Question 141. The period of a satellite in a circular orbit of eradius R is T, and the period of another satellite in a circular orbit of radius 4R is.

1. 4T
2. T/4
3. 8T
4. T/8

Answer: 3. 8T

Question 142. Two planets move around the sun. The periodic times and the mean radii of the orbits are T₁, T₂ and r₁, r₂ respectively. The ratio T₁/ T₂ is equal to –

1. (r₁/ r₂)^1/2
2. r₁/ r₂
3. (r₁/ r₂)²
4. (r₁/ r₂)^3/2

Answer: 4. (r₁/ r₂)^3/2

Question 143. The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be –

1. 83 minute
2. 83 × \(\sqrt{8}\) minutes
3. 664 minutes
4. 249 minutes

Answer: 3. 664 minutes

Question 144. A satellite of mass m is circulating around the earth with constant angular velocity. If the radius of the orbit is R₀ and the mass of the earth is M, the angular momentum about the centre of the earth is –

1. \(\mathrm{m} \sqrt{G M R_0}\)
2. \(\mathrm{M} \sqrt{G M R_0}\)
3. \(\mathrm{m} \sqrt{\frac{G M}{R_0}}\)
4. \(\mathrm{M} \sqrt{\frac{G M}{R_0}}\)

Answer: 1. \(\mathrm{m} \sqrt{G M R_0}\)

Question 145. A planet revolves around the sun whose mean distance is 1.588 times the mean distance between the earth and the sun. The revolution time of the planet will be –

1. 1.25 years
2. 1.59 years
3. 0.89 years
4. 2 years

Answer: 4. 2 years

Question 146. If the mass of a satellite is doubled and the time period remains constant the ratio of orbit in the two cases will be –

1. 1: 2
2. 1: 1
3. 1 : 3
4. None of these

Answer: 2. 1:1

Question 147. The earth revolves around the sun in one year. If the distance between them becomes double, the new period of revolution will be –

1. 1/2 years
2. \(2 \sqrt{2}\) years
3. 4 years
4. 8 years

Answer: 2. \(2 \sqrt{2}\) years

Question 148. A body revolved around the sun 27 times faster than the earth what is the ratio of their radii

1. 1/3
2. 1/9
3. 1/27
4. 1/4

Answer: 2. 1/9

Question 149. The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be –

1. 16 L
2. 64 L
3. \(\frac{L}{4}\)
4. 4 L

Answer: 4. 4 L

Question 150. The ratio of the distance of two planets from the sun is 1.38. The ratio of their period of revolution around the sun is –

1. 1.38
2. 1.38^3/2
3. 1.38^1/2
4. 1.38³

Answer: 2. 1.38^3/2

Question 151. Kepler’s second law (law of areas) is nothing but a statement of –

1. Work energy theorem
2. Conservation of linear momentum
3. Conservation of angular momentum
4. Conservation of energy

Answer: 3. Conservation of angular momentum

Question 152. In an elliptical orbit under gravitational force, in general.

1. Tangential velocity is constant
2. Angular velocity is constant
3. Radial velocity is constant
4. Areal velocity is constant

Answer: 4. Areal velocity is constant

Question 153. What does not change in the field of central force?

1. Potential energy
2. Kinetic energy
3. Linear momentum
4. Angular momentum

Answer: 4. Angular momentum

Question 154. A planet is moving in an elliptic orbit. If T, V, E, L stand respectively for their kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following statements is correct

1. T is conserved
2. V is always positive
3. E is always negative
4. L is conserved but the direction of the vector changes continuously

Answer: 3. E is always negative

Question 155. Three identical stars of mass M are located at the vertices of an equilateral triangle with side L. The speed at which they will move if they all revolve under the influence of one another’s gravitational force in a circular orbit circumscribing the triangle while still preserving the equilateral triangle :

1. \(\sqrt{\frac{2 G M}{L}}\)
2. \(\sqrt{\frac{G M}{L}}\)
3. \(2 \sqrt{\frac{G M}{L}}\)
4. Not possible at all

Answer: 2. \(\sqrt{\frac{G M}{L}}\)

Question 156. Periodic-time of a satellite revolving very near to the surface of the earth is – (ρ is the density of the earth)

1. Proportional to \(\frac{1}{\rho}\)
2. Proportional to \(\frac{1}{\sqrt{\rho}}\)
3. Proportional ρ
4. Does not depend on ρ.

Answer: 2. Proportional to \(\frac{1}{\sqrt{\rho}}\)

Question 157. A satellite is moving around the earth. In order to make it move to infinity, its velocity must be increased by

1. 20%
2. It is impossible to do so
3. 82.8%
4. 41.4%

Answer: 4. 41.4%

Question 158. If the radius of the earth is to decrease by 4% and its density remains the same, then its escape velocity will

1. Remain same
2. Increase by 4%
3. Decrease by 4%
4. Increase by 2%

Answer: 3. Decrease by 4%

Question 159. An earth satellite is moved from one stable circular orbit to another higher stable circular orbit. Which one of the following quantities increases for the satellite as a result of this change

1. Gravitational force
2. Gravitational potential energy
3. Centripetal acceleration
4. Linear orbital speed

Answer: 2. Gravitational potential energy

Question 160. The relay satellite transmits the television programme continuously from one part of the world to another because its

1. A period is greater than the period of rotation of the earth
2. Period is less than the period of rotation of the earth about its axis
3. Period has no relation with the period of the earth about its axis
4. Period is equal to the period of rotation of the earth about its axis

Answer: 4. Period is equal to the period of rotation of the earth about its axis

Question 161. If the universal constant of gravitation were decreasing uniformly with time, then a satellite in orbit would still maintain its

1. Radius
2. Tangential speed
3. Angular momentum
4. Period of revolution

Answer: 3. Angular momentum

Question 162. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth :

1. The acceleration of S is always directed towards the centre of the earth
2. The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
3. The total mechanical energy of S varies periodically with time
4. The linear momentum of S remains constant in magnitude.

Answer: 1. The acceleration of S is always directed towards the centre of the earth

Question 163. The moon revolves around the Earth 13 times in one year. If the ratio of sun-earth distance to earth-moon distance is 392, then the ratio of masses of sun and earth will be

1. 3.56 × 10⁵
2. 3.56 × 10⁶
3. 3.56 × 10⁷
4. 3.56 × 10⁸

Answer: 1. 3.56 × 10⁵

Question 164. The earth revolves around the sun in an elliptical orbit. If \(\frac{O A}{O B}\)= x, the ratio of speeds of earth at B and A will be

1. x
2. \(\sqrt{x}\)
3. x2
4. \(x \sqrt{x}\)

Answer: 1. x

Question 165. The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

1. 10 h
2. 80 h
3. 40 h
4. 20 h

Answer: 3. 40 h

Question 166. If two spheres of the same masses and radius are brought in contact, then the force of attraction between them will be proportional to (for a given density ρ) :

1. r²
2. r³
3. r⁶
4. r⁴

Answer: 4. r⁴

Question 167. Assume the earth to be a sphere of radius R. If g is the acceleration due to gravity at any point on the earth’s surface, the mass of the earth is :

1. \(\frac{g R}{G}\)
2. \(\frac{g^2 R^2}{G}\)
3. \(\frac{g R^2}{G}\)
4. \(\frac{g^2 R}{G}\)

Answer: 3. \(\frac{g R^2}{G}\)

Question 168. Energy required to transfer a 400 kg satellite in a circular orbit of radius 2 R to a circular orbit of radius 4 R, where R is the radius of the earth. [Given g = 9.8 ms^-2, R = 6.4 × 10⁶ m]

1. 1.65 × 10⁹ J
2. 3.13 × 10⁹ J
3. 6.26 × 10⁹ H
4. 4.80 × 10⁹ J

Answer: 2. 3.13 × 10⁹ J

Question 169. Suppose the gravitational force varies inversely as the 4th power of the distance. If a satellite describes a circular orbit of radius R under the influence of this force, then the time period T of the orbit is proportional to

1. R^3/2
2. R^5/2
3. R²
4. R^7/2

Answer: 2. R^5/2

Question 170. A double star system consists of two stars A and B which have time periods T_A and T_B. Radius R_A and R_B and mass M_A and M_B. Choose the correct option.

1. If T_A> T_B then R_A> R_B
2. If T_A> T_B then M_A> M_B
3. \(\left(\frac{T_A}{T_B}\right)^2=\left(\frac{R_A}{R_B}\right)^3\)
4. T_A = T_B

Answer: 4. T_A = T_B

Question 171. Mass M is uniformly distributed only on the curved surface of a thin hemispherical shell. A, B and C are three points on the circular base of a hemisphere, such that A is the centre. Let the gravitational potential at points A, B and C be V_A, V_B, V_C respectively. Then

1. V_A> V_B>V_C
2. V_C> V_B>V_A
3. V_B>V_A and V_B> V_C
4. V_A= V_B=V_C

Answer: 4. V_A= V_B=V_C

Question 172. The figure shows the elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1is the time for the planet to move from C to D and t₂ is the time to move from A to B, then:

1. t₁> t₂
2. t₁= 4t₂
3. t₁= 2t₂
4. t₁= t₂

Answer: 3. t₁= 2t₂

Question 173. A particle of mass M is situated at the centre of a spherical shell of the same mass and radius a. The gravitational potential at a point situated at \(\frac{a}{2}\) distance from the centre, will be

1. \(-\frac{3 G M}{a}\)
2. \(-\frac{2 G M}{a}\)
3. \(-\frac{G M}{a}\)
4. \(-\frac{4 G M}{a}\)

Answer: 1. \(-\frac{3 G M}{a}\)

Question 174. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R₁ to another of radius R₂(R₂> R₁) is

1. \(G m M\left(\frac{1}{R_1^2}-\frac{1}{R_2^2}\right)\)
2. \({GmM}\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\)
3. \(-\frac{G M}{a}\)
4. \(-\frac{4 G M}{a}\)

Answer: 4. \(-\frac{4 G M}{a}\)

Question 175. The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be

1. \(\frac{3 V}{4}\)
2. 6V
3. 12 V
4. \(\frac{3 V}{2}\)

Answer: 2. 6V

Question 176. The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in the figures below. The correct figure is.

Answer: 4

Question 177. A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio \(\frac{v_1}{v_2}\) is:

1. (r₁/r₂)²
2. r₂/r₁
3. (r₂/r₁)²
4. r₁/r₂

Answer: 2. r₂/r₁

Question 178. A body projected vertically from the Earth reaches a height equal to the earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest :

1. At the highest position of the body
2. At the instant just before the body hits the earth
3. It remains constant all through
4. At the instant just after the body is projected

Answer: 2. At the instant just before the body hits the earth

Question 179. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is :

1. \(\sqrt{\frac{2 G M}{R}}\)
2. \(\sqrt{\frac{2 G M}{R^2}}\)
3. \(\sqrt{2 g R^2}\)
4. \(\sqrt{\frac{2 G M}{R^2}}\)

Answer: 1. \(\sqrt{\frac{2 G M}{R}}\)

Question 180. A particle of mass M is situated at the centre of a spherical shell of mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be:

1. \(\frac{2 G M}{a}\)
2. \(\frac{3 G M}{a}\)
3. \(\frac{4 G M}{a}\)
4. \(\frac{G M}{a}\)

Answer: 2. \(\frac{3 G M}{a}\)

Question 181. Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R ? (r is measured from the centre of the spherical shell)

Answer: 2

Question 182. The height at which the weight of a body becomes 1/16th, its weight on the surface of the earth (radius R), is :

1. 5R
2. 15R
3. 3R
4. 4R

Answer: 3. 3R

Question 183. A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to :

1. 4GMP/DP²
2. GMPm/DP²
3. GMP/DP²
4. 4GMPm/DP²

Answer: 1. 4GMP/DP²

Question 184. A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R is the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is :

1. 5
2. 10
3. \(6 \sqrt{2}\)
4. \(\frac{6}{\sqrt{2}}\)

Answer: 3. \(6 \sqrt{2}\)

Question 185. A body of mass ‘m’ is taken from the earth’s surface to a height equal to twice the radius (R) of the earth. The change in potential energy of the body will be:

1. \(\frac{2}{3} m g R\)
2. 3mgR
3. \(\frac{1}{3} m g R\)
4. mg2R

Answer: 1. \(\frac{2}{3} m g R\)

Question 186. Infinite number of bodies, each of mass 2 kg are situated on the x-axis at distances 1m, 2m, 4m, 8m, …….. respectively, from the origin. The resulting gravitational potential due to this system at the origin will be :

1. \(-\frac{8}{3} G\)
2. \(-\frac{4}{3} G\)
3. –4G
4. – G

Answer: 3. –4G

Question 187. A block hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98×10²⁴ kg) have to be compressed to be a black hole?

1. 10^-9 m
2. 10^-6 m
3. 10^-2 m
4. 100 m

Answer: 3. 10^-2 m

Question 188. Dependence of intensity of gravitational field (E) of the earth with distance (r) from the centre of the earth is correctly represented by:

Answer: 1

Question 189. Kepler’s third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of average distance r between the sun and planet i.e. T² = Kr³ here K is constant. If the masses of the sun and planet are M and m respectively then as per Newton’s law of gravitation force of attraction between them is \(\mathrm{F}=\frac{G M m}{r^2}\) r, here G is gravitational constant. The relation between G and K is described as:

1. GMK = 4π²
2. K = G
3. \(\mathrm{K}=\frac{1}{G}\)
4. GK = 4π²

Answer: 1. GMK = 4π²

Question 190. A remote-sensing satellite of the earth revolves in a circular orbit at a height of 0.25 × 10⁶ m above the surface of the earth. If the earth’s radius is 6.38 × 10⁶ m and g = 9.8 ms^-2, then the orbital speed of the satellite is :

1. 8.56 km s^-1
2. 9.13 km s^-1
3. 6.67 km s^-1
4. 7.76 km s^-1

Answer: 4. 7.76 km s^-1

Question 191. At what height from the surface of the earth are the gravitational potential and the value of g –5.4 × 107 J kg^-2 and 6.0 ms^-2 respectively? Take the radius of the earth as 6400 km.

1. 2000 km
2. 2600 km
3. 1600 km
4. 1400 km

Answer: 2. 2600 km

Question 192. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

1. The total mechanical energy of S varies periodically with time.
2. The linear momentum of S remains constant in magnitude.
3. The acceleration of S is always directed towards the centre of the earth.
4. The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.

Answer: 3. The acceleration of S is always directed towards the centre of the earth.

Question 193. The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and mean density are twice that of earth is:

1. \(1: \sqrt{2}\)
2. 1: 2
3. \(1: 2 \sqrt{2}\)
4. 1: 4

Answer: 3. \(1: 2 \sqrt{2}\)

Question 194. Starting from the centre of the earth having radius r, the variation of g (acceleration due to gravity) is shown by

Answer: 3

Question 195. A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth’s surface, is

1. \(-\frac{2 m g_0 R^2}{R+h}\)
2. \(\frac{\mathrm{mg}_0 \mathrm{R}^2}{2(\mathrm{R}+\mathrm{h})}\)
3. \(-\frac{m g_0 R^2}{2(R+h)}\)
4. \(\frac{\mathrm{Rmg}_0 \mathrm{R}^2}{\mathrm{R}+\mathrm{h}}\)

Answer: 3. \(-\frac{m g_0 R^2}{2(R+h)}\)

Question 196. A physical quantity of the dimensions of length that can be formed out of c, G and \(\frac{e^2}{4 \pi \epsilon_0}\) is the velocity of light, G is a universal constant of gravitation and e is charge] :

1. \(\frac{1}{c^2}\left[G \frac{e^2}{4 \pi \epsilon_0}\right]^{1 / 2}\)
2. \(c^2\left[G \frac{e^2}{4 \pi \epsilon_0}\right]^{1 / 2}\)
3. \(\frac{1}{c^2}\left[\frac{e^2}{G 4 \pi \epsilon_0}\right]^{1 / 2}\)
4. \(\frac{1}{c} G \frac{e^2}{4 \pi \epsilon_0}\)

Answer: 1. \(\frac{1}{c^2}\left[G \frac{e^2}{4 \pi \epsilon_0}\right]^{1 / 2}\)

Question 197. Suppose the charge of a proton and an electron differ slightly. One of them is – e, and the other is (e + Δe). If the net of electrostatic force and the gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given the mass of hydrogen mh = 1.67 × 10^-27 kg]

1. 10^-20 C
2. 10^-23 C
3. 10^-37 C
4. 10^-47 C

Answer: 3. 10^-37 C

Question 198. Two astronauts are floating in gravitational-free space after having lost contact with their spaceship. The two will :

1. Keep floating at the same distance between them
2. Move towards each other
3. Move away from each other
4. Will become stationary

Answer: 2. Move towards each other

Question 199. The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AB at the position of the Sun S as shown in the figure. Then

1. K_A < K_B < K_C
2. K_B > K_A > K_C
3. K_B < K_A < K_C
4. K_A > K_B > K_C

Answer: 4. K_A > K_B > K_C

Question 200. If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

1. Raindrops will fall faster.
2. ‘g’ on the Earth will not change
3. Time period of a simple pendulum on the Earth would decrease.
4. Walking on the ground would become more difficult.

Answer: 2. ‘g’ on the Earth will not change

Question 201. The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

1. \(\frac{3}{2} \mathrm{mgR}\)
2. mgR
3. 2 mgR
4. \(\frac{1}{2} \mathrm{mgR}\)

Answer: 4. \(\frac{1}{2} \mathrm{mgR}\)

Question 202. The time period of a geostationary satellite is 24 h, at a height of 6R_E (R_E is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is 2.5 R_E from the surface will be :

1. \(6 \sqrt{2} h\)
2. \(12 \sqrt{2} h\)
3. \(\frac{24}{2.5} h\)
4. \(\frac{12}{2.5} h\)

Answer: 1. \(6 \sqrt{2} h\)

Question 203. Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final – initial) of an object of mass m, when taken to a height h from the surface of the earth (of radius R), is given by :

1. \(-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}\)
2. \(\frac{\mathrm{GMmh}}{\mathrm{R}(\mathrm{R}+\mathrm{h})}\)
3. mgh
4. \(\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}\)

Answer: 2. \(\frac{\mathrm{GMmh}}{\mathrm{R}(\mathrm{R}+\mathrm{h})}\)

Question 204. A body weight of 72N on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth?

1. 24N
2. 48 N
3. 32 N
4. 30 N

Answer: 3. 32 N

Question 205. The escape velocity from the Earth’s surface is υ. The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is:

1. 2υ
2. 3υ
3. 4υ
4. υ

Answer: 3. 4υ

Question 206. A particle of mass ‘m’ is projected with a velocity u = kV_e (k < 1) from the surface of the earth. (V_e = escape velocity) The maximum height above the surface reached by the particle is

1. \(\mathrm{R}\left(\frac{\mathrm{k}}{1+\mathrm{k}}\right)^2\)
2. \(\frac{\mathrm{R}^2 \mathrm{k}}{1+\mathrm{k}}\)
3. \(\frac{\mathrm{Rk}^2}{1-\mathrm{k}^2}\)
4. \(R\left(\frac{k}{1-k}\right)^2\)

Answer: 3. \(\frac{\mathrm{Rk}^2}{1-\mathrm{k}^2}\)

Question 207. The height at which the acceleration due to gravity becomes \(\) (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

1. \(\frac{R}{\sqrt{2}}\)
2. \(\frac{R}{2}\)
3. \(\sqrt{2} R\)
4. 2R

Answer: 4. 2R

Question 208. Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1. Zero
2. \(-\frac{4 G m}{r}\)
3. \(-\frac{6 G m}{r}\)
4. \(-\frac{9 G m}{r}\)

Answer: 4. \(-\frac{9 G m}{r}\)

Question 209. Two particles of equal mass ‘m’ go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to its centre of mass is:

1. \(\sqrt{\frac{G m}{4 R}}\)
2. \(\sqrt{\frac{G m}{3 R}}\)
3. \(\frac{G m M}{2 R}\)
4. \(\frac{G m M}{3 R}\)

Answer: 1. \(\sqrt{\frac{G m}{4 R}}\)

Question 210. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

1. \(\frac{5 G m M}{6 R}\)
2. \(\frac{2 G m M}{3 R}\)
3. \(\frac{G m M}{2 R}\)
4. \(\frac{G m M}{3 R}\)

Answer: 1. \(\frac{5 G m M}{6 R}\)

Question 211. Four particles, each of mass M and equidistant from each other move along a circle of radius R under the action of their mutual gravitational attraction. the speed of each particle is:

1. \(\sqrt{\frac{G M}{R}}\)
2. \(\sqrt{2 \sqrt{2} \frac{G M}{R}}\)
3. \(\sqrt{\frac{G M}{R}(1+2 \sqrt{2})}\)
4. \(\frac{1}{2} \sqrt{\frac{G M}{R}(1+2 \sqrt{2})}\)

Answer: 4. \(\frac{1}{2} \sqrt{\frac{G M}{R}(1+2 \sqrt{2})}\)

Question 212. From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is :(G = gravitational constant)

1. \(\frac{-G M}{2 R}\)
2. \(\frac{-G M}{R}\)
3. \(\frac{-2 G M}{3 R}\)
4. \(\frac{-2 G M}{R}\)

Answer: 2. \(\frac{-G M}{R}\)

Question 213. If the angular momentum of a planet of mass m, moving around the sun in a circular orbit is L, about the centre of the Sun, its areal velocity is:

1. \(\frac{2 L}{m}\)
2. \(\frac{4 \mathrm{~L}}{\mathrm{~m}}\)
3. \(\frac{L}{2 m}\)
4. \(\frac{\mathrm{L}}{\mathrm{m}}\)

Answer: 3. \(\frac{L}{2 m}\)

Question 214. The energy required to take a satellite to a height ‘h’ above Earth’s surface (radius or Earth = 6.4 × 10³ km) is E₁ and the kinetic energy required for the satellite to be in a circular orbit at this height is E₂. The value of h for which E₁ and E₂ are equal is :

1. 1.28 × 10⁴ km
2. 6.4 × 10³ km
3. 3.2 × 10³ km
4. 1.6 × 10³ km

Answer: 3. 3.2 × 10³ km

Question 215. A satellite is moving with a constant speed v in a circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is :

1. \(\frac{3}{2} m v^2\)
2. \(\frac{1}{2} m v^2\)
3. 2mv²
4. mv²

Answer: 4. mv²

Question 216. Two stars of masses 3 × 10³¹ kg each, and at distance 2 × 10¹¹ m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that a meteorite should have at O is (Take Gravitational constant G = 6.67 × 10^-11 Nm2 kg^-2) What is the order of energy of the gas due to its thermal motion?

1. 3.8 × 10⁴ m/s
2. 1.4 × 10⁵ m/s
3. 2.8 × 10⁵ m/s
4. 2.4 × 10⁴ m/s

Answer: 3. 2.8 × 10⁵ m/s

Question 217. A satellite is revolving in a circular orbit at a height h from the earth’s surface, such that h<<R where R is the radius of the earth. Assuming that the effect of the earth’s atmosphere can be neglected. The minimum increase in the speed required so that the satellite could escape from the gravitational field of the earth is :

1. \(\sqrt{g R}(\sqrt{2}-1)\)
2. \(\sqrt{\frac{g R}{2}}\)
3. \(\sqrt{2 \mathrm{gR}}\)
4. \(\sqrt{g R}\)

Answer: 1. \(\sqrt{g R}(\sqrt{2}-1)\)

Question 218. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be: 

1. \(\frac{3}{2} s\)
2. \(\frac{2}{\sqrt{3}} \mathrm{~s}\)
3. \(\frac{\sqrt{3}}{2} s\)
4. \(2 \sqrt{3} \mathrm{~s}\)

Answer: 4. \(2 \sqrt{3} \mathrm{~s}\)

Question 219. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass ‘m’ at x = 0, if the mass per unit length of the rod is A + Bx², is given by

1. \(G m\left[A\left(\frac{1}{a+L}-\frac{1}{a}\right)-B L\right]\)
2. \({Gm}\left[A\left(\frac{1}{a+L}-\frac{1}{a}\right)+B L\right]\)
3. \({Gm}\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)+B L\right]\)
4. \(G m\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)-B L\right]\)

Answer: 3. \({Gm}\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)+B L\right]\)

Question 220. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. the subsequent motion of the combined body will be :

1. In the same circular orbit of radius R
2. Such that it escapes to infinity
3. In an elliptical orbit
4. In a circular orbit of a different radius

Answer: 3. In an elliptical orbit

Question 221. Two satellites, A and B, have masses of m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, \(\frac{T_{\mathrm{A}}}{\mathrm{T}_{\mathrm{B}}}\) is:

1. 1
2. \(\sqrt{\frac{1}{2}}\)
3. 2
4. \(\frac{1}{2}\)

Answer: 1. 1