NEET Physics Class 11 Chapter 4 Elasticity And Viscosity Multiple Choice Question And Answers

Elasticity And Viscosity Solids Multiple Choice Question And Answers

Question 1. The diameter of a brass rod is 4 mm and Young’s modulus of brass is 9 × 10¹⁰ N/m². The force required to stretch by 0.1% of its length is:

1. 360 πN
2. 36 N
3. 144 π × 10³ N
4. 36 π × 10⁵ N

Answer: 1. 360 πN

Question 2. A steel wire is suspended vertically from a rigid support. When loaded with a weight in the air, it expands by L_a and when the weight is immersed completely in water, the extension is reduced to L_w. The relative density of the material of the weight is

1. \(\frac{L_a}{L_a-L_w}\)
2. \(\frac{\mathrm{L}_{\mathrm{w}}}{\mathrm{L}_{\mathrm{a}}}\)
3. \(\frac{\mathrm{L}_{\mathrm{a}}}{\mathrm{L}_{\mathrm{w}}}\)
4. \(\frac{L_w}{L_a-L_w}\)

Answer: 2. 1. \(\frac{L_a}{L_a-L_w}\)

Question 3. Two wires of equal length and cross-section area are suspended as shown in the figure. Their Young’s modulus is Y₁ and Y₂ respectively. The equivalent of Young’s modulus will be

1. Y1 + Y₂
2. \(\frac{Y_1+Y_2}{2}\)
3. \(\frac{Y_1 Y_2}{Y_1+Y_2}\)
4. \(\sqrt{Y_1 Y_2}\)

Answer: 2. \(\frac{Y_1+Y_2}{2}\)

Question 4. The load versus elongation graph for four wires of the same materials is shown in the figure. The thinnest wire is represented by the line :

1. OC
2. OD
3. OA
4. OB

Answer: 3. OA

Question 5. A force F is needed to break a copper wire having radius R. Then the force needed to break a copper wire of radius 2 R will be :

1. F/2
2. 2 F
3. 4 F
4. F/4

Answer: 3. 4 F

Question 6. A brass rod of length 2 m and a cross-sectional area of 2.0 cm² is attached end to end to a steel rod of length L and a cross-sectional area of 1.0 cm². The compound rod is subjected to equal and opposite pulls of magnitude 5 × 10⁴ N at its ends. If the elongations of the two rods are equal, then the length of the steel rod (L) is

(Y_Brass = 1.0 × 10¹¹ N/m² and Y_Steel = 2.0 × 1011 N/m² )

1. 1.5 m
2. 1.8 m
3. 1 m
4. 2 m

Answer: 4. 2 m

Question 7. If the ratio of lengths, radii, and Young’s moduli of steel and brass wires in the figure are a, b, and c respectively. Then the corresponding ratio of increase in their lengths would be :

1. \(\frac{2 \mathrm{ac}}{\mathrm{b}^2}\)
2. \(\frac{3 a}{2 b^2 c}\)
3. \(\frac{3 c}{2 a b^2}\)
4. \(\frac{2 a^2 c}{b}\)

Answer: 2. \(\frac{3 a}{2 b^2 c}\)

Question 8. The breaking stress of a wire depends upon

1. Length of the wire
2. The radius of the wire
3. Material of the wire
4. The shape of the cross-section

Answer: 3. Material of the wire

Question 9. The mean distance between the atoms of iron is 3 ×10^-10 m and the interatomic force constant for iron is 7 N /m. Yong’s modulus of elasticity for iron is

1. 2.33 × 10⁵ N/ m²
2. 23.3 × 10¹⁰ N/ m²
3. 233 × 10¹⁰N/ m²
4. 2.33 × 10¹⁰ N/ m²

Answer: 4. 2.33 × 1010 N/ m²

Question 10. An iron rod of length 2m and cross-section area of 50mm² stretched by 0.5mm, when a mass of 250kg is hung from its lower end. Young’s modulus of the iron rod is

1. 19.6 ×10¹⁰ N/ m²
2. 19.6 × 10¹⁵ N/ m²
3. 19.6 × 10¹⁸ N/ m²
4. 19.6 × 10²⁰ N/ m²

Answer: 1. 19.6 ×1010 N/ m²

Question 11. A steel wire of 1 m long and 1 mm² cross-section area is hung from a rigid support. When a weight of 1 kg is hung from it then the change in length will be (given Y = 2 × 10¹¹ N / m²)

1. 0.5 mm
2. 0.25 mm
3. 0.05 mm
4. 5 mm

Answer: 3. 0.05 mm

Question 12. A 1m long metal wire of cross-sectional area 10^-6 m² is fixed at one end from a rigid support and a weight W is hanging at its other end. The graph shows the observed extension of length Δl of the wire as a function of W. Young’s modulus of the material of the wire in SΙ units is

1. 5 × 10⁴
2. 2 × 10⁵
3. 2 × 10¹¹
4. 5 × 10¹¹

Answer: 3. 2 × 10¹¹

Question 13. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is :

1. 0.25
2. 0.50
3. 2.00
4. 4.00

Answer: 3. 2.00

Question 14. The Young’s modulus of a wire of length (L) and radius (r) is Y. If the length is reduced to \(\frac{\mathrm{L}}{2}\) and radius to \(\frac{\mathrm{R}}{2}\) then its Young’s modulus will be

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

Answer: 2. Y

Question 15. A 5m aluminium wire (Y = 7 × 10¹⁰ N/m²) of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire (Y= 12 × 10¹⁰ N/m²) of the same length under the same weight, the diameter should be in mm

1. 1.75
2. 2.0
3. 2.3
4. 5.0

Answer: 3. 2.3

Question 16. The following four wires are made of the same material and the same tension is applied to them. Which one will have the maximum increase in length?

1. Length = 100 cm, Diameter = 1mm
2. Length = 50 cm, Diameter = 0.5 mm
3. Length = 200 cm, Diameter = 2mm
4. Length = 300 cm, Diameter = 3 mm

Answer: 2. Length = 50 cm, Diameter = 0.5 mm

Question 17. A catapult’s string made of rubber has a cross-section area of 25 mm2 and a length of 10 cm. To throw a 5 gm pabble it is stretched up to 5 cm and released. The velocity of the projected pabble is (Young coefficient of elasticity of rubber is 5 × 10⁸ N/m²) :

1. 20 m/s
2. 100 m/s
3. 250 m/s
4. 200 m/s

Answer: 3. 250 m/s

Question 18. The diameter of a brass rod is 4 mm and the Young modulus of elasticity is 9 × 10¹⁰ N/m². The force required to increase the length of the rod by 0.10% will be :

1. 360 πN
2. 36 N
3. 144π × 10³ N
4. 36π × 10⁵ N

Answer: 1. 360 πN

Question 19. Two blocks each of mass 2kg are connected as shown in the figure. The breaking stress of the material of the wire is \(\frac{2}{\pi} \times 10^9\) N/m². Find the minimum radius of the wire used if it is not to break.

1. 10^-3 m
2. 10^-4 m
3. 10^-5 m
4. 10^-6 m

Answer: 2. 10^-4 m

Question 20. Four wires of the same material are stretched by the same load. The dimensions of the wires are given below. The one that has the maximum elongation is of

1. Diameter 1 mm and length 1 m
2. Diameter 2 mm and length 2 m
3. Diameter 0.5 mm and length 0.5 m
4. Diameter 3 mm and length 3 m

Answer: 3. Diameter 0.5 mm and length 0.5 m

Question 21. An elevator cable can have a maximum stress of 7 × 10⁷ N/m² for appropriate safety factors. Its maximum upward acceleration is 1.5 m/s². If the cable has to support the total weight of 2000 kg of a loaded elevator, the minimum area of the cross-section of the cable should be (g = 10 m/s²)

1. 3.28 cm²
2. 2.38 cm²
3. 0.328 cm²
4. 8.23 cm²

Answer: 1. 3.28 cm²

Question 22. A 2m long light metal rod AB is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One wire is of brass and has a cross-sectional area of 0.2 × 10^-4 m² and the other is of steel with 0.1 × 10^-4 m² cross-sectional area. in order to have equal stresses in the two wires, a weight W is hung from the rod. The position of the weight along the rod from end A should be

1. 66.6 cm
2. 133 cm
3. 44.4 cm
4. 155.6 cm

Answer: 1. 66.6 cm

Question 23. A brass rod of length 2 m and a cross-sectional area of 2.0 cm² is attached end to end to a steel rod of length L and a cross-sectional area of 1.0 cm². The compound rod is subjected to equal and opposite pulls of magnitude 5 × 10⁴ N at its ends. If the elongations of the two rods are equal, then the length of the steel rod (L) is (Y_Brass = 1.0 × 10¹¹ N/m² and Y_Steel = 2.0 × 10¹¹ N/m² )

1. 1.5 m
2. 1.8 m
3. 1 m
4. 2 m

Answer: 4. 2m

Question 24. A square brass plate of side 1.0 m and thickness 0.005 m is subjected to a force F on its smaller opposite edges, causing a displacement of 0.02 cm. If the shear modulus of brass is 0.4 × 10¹¹ N/m², the value of the force F is

1. 4 × 10³ N
2. 400 N
3. 4 × 10⁴ N
4. 1000 N

Answer: 3. 4 × 10⁴ N

Question 25. A solid cylinder of radius r and length l is clamped at its upper end and the lower end is twisted through θ. The shear strain is given by.

1. θ
2. \(\frac{\theta \ell}{\mathrm{r}}\)
3. \(\frac{\theta \mathrm{r}}{\ell}\)
4. 0

Answer: 3. \(\frac{\theta \mathrm{r}}{\ell}\)

Question 26. A 50 kg motor rests on four cylindrical rubber blocks. Each block has a height of 4 cm and a cross-sectional area of 16 cm². The shear modulus of rubber is 2 × 10⁶ N/m². A sideways force of 500 N is applied to the motor. The distance that the motor moves sideways is

1. 0.156 cm
2. 1.56 cm
3. 0.312 cm
4. 0.204 cm

Answer: 1. 0.156 cm

Question 27. If the poison ratio is 0.4 and after increasing the length of the wire by 0.05% then the decrease in its diameter will be :

1. 0.02%
2. 0.1%
3. 0.01%
4. 0.4%

Answer: 1. 0.02%

Question 28. A 50 kg motor rests on four cylindrical rubber blocks. Each block has a height of 4 cm and a cross-sectional area of 16 cm². The shear modulus of rubber is 2 × 10⁶ N/m². A sideways force of 500 N is applied to the motor. The distance that the motor moves sideways is

1. 0.156 cm
2. 1.56 cm
3. 0.312 cm
4. 0.204 cm

Answer: 1. 0.156 cm

Question 29. A metal block is experiencing an atmospheric pressure of 1 × 10⁵ N/m², when the same block is placed in a vacuum chamber, the fractional change in its volume is (the bulk modulus of metal is 1.25 × 10¹¹ N/m²)

1. 4 × 10^-7
2. 2 × 10^-7
3. 8 × 10^-7
4. 1 × 10^-7

Answer: 3. 8 × 10^-7

Question 30. The compressibility of water is 46.4 × 10^-6/atm. This means that

1. The bulk modulus of water is 46.4 × 10⁶ atm
2. The volume of water decreases by 46.4 one-millionths of the original volume for each atmosphere increase in pressure
3. When water is subjected to an additional pressure of one atmosphere, its volume decreases by 46.4%
4. When water is subjected to an additional pressure of one atmosphere, its volume is reduced to 10^-6 of its original volume.

Answer: 2. The volume of water decreases by 46.4 one-millionths of the original volume for each atmosphere increase in pressure

Question 31. If a rubber ball is taken at a depth of 200 m in a pool its volume decreases by 0.1%. If the density of the water is 1 × 10³ kg/m³ and g = 10 m/s², then the volume elasticity in N/m² will be :

1. 108
2. 2 × 108
3. 109
4. 2 × 109

Answer: 4. 2 × 109

Question 32. Two wires of the same material and length but diameter in the ratio 1: 2 are stretched by the same force. The ratio of potential energy per unit volume for the two wires when stretched will be:

1. 1: 1
2. 2: 1
3. 4: 1
4. 16: 1

Answer: 4. 16:1

Question 33. Two wires A and B of the same length and of the same material have the respective radii r₁ and r₂. One end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

1. \(\frac{r_1^2}{r_2^2}\)
2. \(\frac{r_2^2}{r_1^2}\)
3. \(\frac{r_2^4}{r_1^4}\)
4. \(\frac{r_1^4}{r_2^4}\)

Answer: 3. \(\frac{r_2^4}{r_1^4}\)

Question 34. The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30°. Then angle of the shear is

1. 12°
2. 0.12°
3. 1.2 °
4. 0.012°

Answer: 2. 0.12°

Question 35. A 2m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be

1. 0.002
2. 0.004
3. 0.008
4. 0.016

Answer: 2. 0.004

Question 36. The relation between γ, η, and K for an elastic material is

1. \(\frac{1}{\eta}=\frac{1}{3 \gamma}+\frac{1}{9 K}\)
2. \(\frac{1}{\mathrm{~K}}=\frac{1}{3 \gamma}+\frac{1}{9 \eta}\)
3. \(\frac{1}{\gamma}=\frac{1}{3 K}+\frac{1}{9 \eta}\)
4. \(\frac{1}{\gamma}=\frac{1}{3 \eta}+\frac{1}{9 K}\)

Answer: 4. \(\frac{1}{\gamma}=\frac{1}{3 \eta}+\frac{1}{9 K}\)

Question 37. The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30º. The angle of the shear is

1. 12º
2. 0.12º
3. 1.2º
4. 0.012º

Answer: 2. 0.12º

Question 38. A rubber ball is brought into 200 m deep water, its volume is decreased by 0.1% then the volume elasticity modulus of the material of the ball will be :

1. 19.6 × 10⁸ N/m²
2. 19.6 × 10^-10 N/m²
3. 19.6 × 10¹⁰ N/m²
4. 19.6 × 10^-8 N/m²

Answer: 1. 19.6 × 10⁸ N/m²

Question 39. The mean density of seawater is ρ, and the bulk modulus is B. The change in density of seawater in going from the surface of the water to a depth h is :

1. \(\frac{\rho g h}{B}\)
2. Bpgh
3. \(\frac{\rho^2 g h}{B}\)
4. \(\frac{B \rho^2}{\mathrm{gh}}\)

Answer: 3. \(\frac{\rho^2 g h}{B}\)

Question 40. A sample of a liquid has an initial volume of 1.5 L. The volume is reduced by 0.2 mL when the pressure increases by 140 kPa. What is the bulk modulus of the liquid?

1. 3.05 × 10⁹ Pa.
2. 1.05 × 10⁹ Pa.
3. 1.05 × 10⁷ Pa.
4. 1.05 × 10¹¹ Pa.

Answer: 2. 1.05 × 10⁹ Pa.

Question 41. If the potential energy of a spring is V on stretching it by 2 cm, its potential energy when it is stretched by 10 cm will be :

1. V/25
2. 5 V
3. V/5
4. 25 V

Answer: 4. 25V

Question 42. If work done in stretching a wire by 1mm is 2J, the work necessary for stretching another wire of the same material, but of double the radius and half the length by 1mm in joule will be –

1. 1/4
2. 4
3. 8
4. 16

Answer: 4. 16

Question 43. According to Hooke’s law of elasticity, if stress is increased, the ratio of stress to strain

1. Increases
2. Decreases
3. Becomes zero
4. Remains constant

Answer: 4. Remains constant

Question 44. Which of the following affects the elasticity of a substance

1. Hammering and annealing
2. Change in temperature
3. Impurity in substance
4. All of these

Answer: 4. All of these

Question 45. Calculate the work done, if a wire is loaded by ‘Mg’ weight and the increase in length is ‘l’

1. Mgl
2. Zero
3. Mgl/2
4. 2Mgl

Answer: 3. Mgl/2

Question 46. An elastic material of Young’s modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is

1. \(\frac{2 Y}{S^2}\)
2. \(\frac{S^2}{2 \mathrm{Y}}\)
3. \(\frac{S}{2 \mathrm{Y}}\)
4. \(\frac{S^2}{Y}\)

Answer: 2. \(\frac{S^2}{2 \mathrm{Y}}\)

Question 47. A stretched rubber has

1. Increased kinetic energy
2. Increased potential energy
3. Decreased kinetic energy
4. Decreased potential energy

Answer: 2. Increased potential energy

Question 48. If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

1. \(\frac{T^2}{2 x}\)
2. \(\frac{\mathrm{T}^2}{2 \mathrm{k}}\)
3. \(\frac{2 x}{T}\)
4. \(\frac{2 T^2}{k}\)

Answer: 2. \(\frac{\mathrm{T}^2}{2 \mathrm{k}}\)

Question 49. On stretching a wire, of length L by l using force F the elastic energy stored per unit volume is

1. Fl/2AL
2. FA/2L
3. FL/2A
4. FL/2

Answer: 1. Fl/2AL

Question 50. A wire of length 50 cm and a cross-sectional area of 1 sq. mm is extended by 1 mm. The required work will be (Y = 2 × 10¹⁰ Nm^-2)

1. 6 × 10^-2 J
2. 4 × 10^-2 J
3. 2 × 10^-2 J
4. 1 × 10^-2 J

Answer: 3. 2 × 10^-2 J

Question 51. When a force is applied on a wire of uniform cross-sectional area 3 × 10^-6 m² and length 4m, the increase in length is 1 mm. Energy stored in it will be (Y = 2 × 1011 N / m²)

1. 6250 J
2. 0.177 J
3. 0.075 J
4. 0.150 J

Answer: 3. 0.075 J

Question 52. The elastic energy stored in a wire of Young’s modulus Y is

1. \(\mathrm{Y} \times \frac{\text { Strain }^2}{\text { Volume }}\)
2. Stress × Strain × Volume
3. \(\frac{\text { Stress }^2 \times \text { Volume }}{2 \mathrm{Y}}\)
4. \(\frac{1}{2} Y \times \text { stress } \times \text { Strain } \times \text { Volume }\)

Answer: 3. \(\frac{\text { Stress }^2 \times \text { Volume }}{2 \mathrm{Y}}\)

Question 53. A wire of length 50 cm and a cross-sectional area of 1 sq. mm is extended by 1 mm. The required work will be (Y = 2 × 10¹⁰ Nm^-2)

1. 6 × 10^-2 J
2. 4 × 10^-2 J
3. 2 × 10^-2 J
4. 1 × 10^-2 J

Answer: 3. 2 × 10^-2 J

Question 54. When a load of 5 kg is hung on a wire then an extension of 3 meters takes place, the work done will be :

1. 75 J
2. 60 J
3. 50 J
4. 100 J

Answer: 1. 75 J

Question 55. When a load of 5 kg is hung on a wire then an extension of 3 metres takes place, the work done will be :

1. 75 J
2. 60 J
3. 50 J
4. 100 J

Answer: 1. 75 J

Question 56. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1mm. Then the elastic energy stored in the wire is?

1. 0.2 J
2. 10J
3. 20J
4. 0.1 J

Answer: 4. 0.1 J

Question 57. If ‘S’ is stress and ‘Y’ is Young’s modulus of the material of a wire, the energy stored in the wire per unit volume is :

1. 2S²Y
2. \(\frac{S^2}{2 \mathrm{Y}}\)
3. \(\frac{2 Y}{S^2}\)
4. \(\frac{S}{2 Y}\)

Answer: 2. \(\frac{S^2}{2 \mathrm{Y}}\)

Question 58. A wire elongates by lmm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)

1. l/2
2. l
3. 2l
4. Zero

Answer: 2. 1

Question 59. An oil drop falls through the air with a terminal velocity of 5 × 10^-4 m/s.

1. The radius of the drop will be :

1. 2.5 × 10^-6 m
2. 2 × 10^-6 m
3. 3 × 10^-6 m
4. 4 × 10^-6 m

Answer: 3. 3 × 10^-6 m

2. The terminal velocity of a drop of half of this radius will be (Viscosity of air = \(\frac{18 \times 10^{-5}}{5}\) N-s/m² density of oil = 900 Kg/m³. Neglect density of air as compared to that of oil).

1. 3.25 × 10^-4 m/s
2. 2.10 × 10^-4 m/s
3. 1.5 × 10^-4 m/s
4. 1.25 × 10^-4 m/s

Answer: 4. 1.25 × 10^-4 m/s

Question 60. The terminal velocity of a sphere moving through a viscous medium is :

1. Directly proportional to the radius of the sphere
2. Inversely proportional to the radius of the sphere
3. Directly proportional to the square of the radius of the sphere
4. Inversely proportional to the square of the radius of a sphere

Answer: 3. Directly proportional to the square of the radius of a sphere

Question 61. A sphere is dropped gently into a medium of infinite extent. As the sphere falls, the net force acting downwards on it

1. Remains constant throughout
2. Increases for some time and then becomes constant
3. Decreases for some time and then becomes zero
4. Increases for some time and then decreases.

Answer: 3. Decreases for some time and then becomes zero

Question 62. A solid sphere falls with a terminal velocity of 10 m/s in air. If it is allowed to fall in a vacuum,

1. Terminal velocity will be more than 10 m/s
2. Terminal velocity will be less than 10 m/s
3. Terminal velocity will be 10 m/s
4. There will be no terminal velocity

Answer: 4. There will be no terminal velocity

Question 63. A spherical ball is dropped in a long column of viscous liquid. Which of the following graphs represents the variation of

1. Gravitational force with time
2. Viscous force with time
3. The net force acting on the ball with time.

1. Q, R, P
2. R, Q, P
3. P, Q, R
4. P, R, Q

Answer: 3. P, Q, R

Question 64. A ball of mass m and radius r is released in a viscous liquid. The value of its terminal velocity is proportional to :

1. \(\frac{1}{r}\)
2. \(\frac{\mathrm{m}}{\mathrm{r}}\)
3. \(\sqrt{\frac{m}{r}}\)
4. m only m

Answer: 2. \(\frac{\mathrm{m}}{\mathrm{r}}\)

Question 65. In Poiseuilli’s method of determination of coefficient of viscosity. the physical quantity that requires greater accuracy in measurement is

1. Pressure difference
2. The volume of the liquid collected
3. Length of the capillary tube
4. Inner radius of the capillary tube

Answer: 4. Inner radius of the capillary tube

Question 66. A viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram

Answer: 3.

Question 67. What is the velocity υ of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η).

1. \(\frac{r^2 g}{9 \eta}(\rho-2 \sigma)\)
2. \(\frac{r^2 g}{9 \eta}(2 \rho-\sigma)\)
3. \(\frac{r^2 g}{9 \eta}(\rho-\sigma)\)
4. \(\frac{2 r^2 g}{9 \eta}(\rho-\sigma)\)

Answer: 1. \(\frac{r^2 g}{9 \eta}(\rho-2 \sigma)\)

Question 68. A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength \(\). When the field is switched off, the drop is observed to fall with terminal velocity 2 × 10^-3 m s^-1. Given g = 9.8 m s^-2, a viscosity of the air = 1.8 × 10^-5 Ns m^-2, and the density of oil ρ = 900 kg m^-3, the magnitude of q is:

1. 1.6 × 10^-19 C
2. 3.2 × 10^-19 C
3. 4.8 × 10^-19 C
4. 8.0 × 10^-19 C

Answer: 4. 8.0 × 10^-19 C

Question 69. A liquid has only

1. Shear modulus
2. Young’s modulus
3. Bulk modulus
4. All of the above

Answer: 3. Bulk modulus

Question 70. According to Newton, viscous force is given by

F = – ηA \(\frac{d v}{d x}\)

where η = coefficient of viscosity, so dimensions of η will be :

1. [ML^-1T^-2]
2. [MLT^-2]
3. [ML^-1T^-1]
4. [M^-1L2T^-2]

Answer: 3. [ML^-1T^-1]

Question 71. Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity ν. The retarding viscous force acting on the spherical ball is:

1. Directly proportional to R but inversely proportional to ν
2. Directly proportional to both radius R and velocity ν
3. Inversely proportional to both radius R and velocity ν
4. Inversely proportional to R but directly proportional to ν

Answer: 2. Directly proportional to both radius R and velocity ν

Question 72. A 20 cm long capillary tube is dipped in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length of the water column in the capillary tube will be :

1. 8 cm
2. 10 cm
3. 4 cm
4. 20 cm

Answer: 4. 20 cm

Question 73. If the terminal speed of a sphere of gold (density = 19.5 kg/m³) is 0.2 m/s in a viscous liquid then find the terminal speed of a sphere of silver (density = 10.5 kg/m³) of the same size in the same liquid (density = 1.5 kg/m³).

1. 0.2 m/s
2. 0.4 m/s
3. 0.133 m/s
4. 0.1 m/s

Answer: 4. 0.1 m/s

Question 74. A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂ (ρ₂< ρ₁). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed ν, i.e., F_viscous= – kν²(k > 0). The terminal speed of the ball is

1. \(\frac{\mathrm{Vg} \rho_1}{\mathrm{k}}\)
2. \(\sqrt{\frac{V g \rho_1}{k}}\)
3. \(\frac{{Vg}\left(\rho_1-\rho_2\right)}{k}\)
4. \(\sqrt{\frac{{Vg}\left(\rho_1-\rho_2\right)}{k}}\)

Answer: 4. \(\sqrt{\frac{{Vg}\left(\rho_1-\rho_2\right)}{k}}\)

Question 75. Two hail stones with radii in the ratio of 1: 2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity will be

1. 1: 1
2. 1: 4
3. 1: 16
4. 1: 32

Answer: 4. 1:32

Question 76. A space is 2.5 cm wide between two large plane surfaces is filled with oil. The force required to drag a very thin plate of area 0.5 m² just midway through the surfaces at a speed of 0.5 m/sec is 1N. The coefficient of viscosity in kg–sec/m² is :

1. 5 × 10^-2
2. 2.5 × 10^-2
3. 1 × 10^-2
4. 7.5 × 10^-2

Answer: 2. 2.5 × 10^-2

Question 77. A raindrop of radius 1.5 mm, experiences a drag force F = (2 × 10^-5 v) N while falling through the air from a height of 2 km, with a velocity v. The terminal velocity of the raindrop will be nearly (use g = 10 m/s²):

1. 200 m/s
2. 60 m/s
3. 7 m/s
4. 3 m/s

Answer: 3. 7 m/s

Question 78. Two identical rods in geometry but of different materials having coefficients of thermal expansion α₁ and α₂ and Young’s moduli Y₁ and Y₂ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If α₁: α₂= 2: 6 the thermal stresses developed in the two rods are equal provided Y₁: Y₂ is equal to :

1. 2 : 3
2. 1: 1
3. 3: 1
4. 4: 9

Answer: 3. 3:1

Question 79. A small steel ball falls through a syrup at a constant speed of 10 cm/s. If the steel ball is pulled upwards with a force equal to twice its effective weight, how fast will it move upwards?

1. 10 cm/s
2. 20 cm/s
3. 5 cm/s
4. – 5 cm/s

Answer: 1. 10 cm/s

Question 80. Two spheres P and Q of equal radii have densities ρ₁ and ρ₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities σ₁ and σ₂ and viscosities η₁ and η₂, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string is taut (see figure). If sphere P alone in L₂ has terminal velocity VPand Q alone in L₁ has terminal velocity VQ, then

1. \(\frac{\left|\vec{V}_{\mathrm{P}}\right|}{\left|\vec{V}_{\mathrm{Q}}\right|}=\frac{\eta_1}{\eta_2}\)
2. \(\frac{\left|\vec{V}_P\right|}{\left|\vec{V}_Q\right|}=\frac{\eta_2}{\eta_1}\)
3. \(\vec{V}_P \cdot \vec{V}_Q>0\)
4. None of these

Answer: 1. \(\frac{\left|\vec{V}_{\mathrm{P}}\right|}{\left|\vec{V}_{\mathrm{Q}}\right|}=\frac{\eta_1}{\eta_2}\)

Question 81. The force required to stretch a steel wire of 1 cm² cross-section to 1.1 times its length, will be (Y = 2 × 10¹¹ Nm^-2)

1. 2 × 10⁶ N
2. 2 × 10³ N
3. 2 × 10^-6 N
4. 2 × 10^-7 N

Answer: 1. 2 × 10⁶ N

Question 82. A cube is subjected to a uniform volume compression. If the side of the cube decreases by 2%, the bulk strain is –

1. 0.02
2. 0.03
3. 0.04
4. 0.06

Answer: 4. 0.06

Question 83. The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

1. length = 100 cm, diameter = 1 mm
2. length = 200 cm, diameter = 2 mm
3. length = 300 cm, diameter = 3 mm
4. length = 50 cm, diameter = 0.5 mm

Answer: 4. length = 50 cm, diameter = 0.5 mm

Question 84. A copper of fixed volume ‘V’ is drawn into a wire of length ‘l’. When this wire is subjected to a constant force ‘F’, the extension produced in the wire is ‘Δl’. Which of the following graph is a straight line?

1. Δl versus 1/l
2. Δl versus l²
3. Δl versus 1/l²
4. Δl versus l

Answer: 2. Δl versus l²

Question 85. The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10^-11 Pa^-1 and the density of water is 10³ kg/m³. What fractional compression of water will be obtained at the bottom of the ocean?

1. 1.0 × 10^-2
2. 1.2 × 10^-2
3. 1.4 × 10^-2
4. 0.8 × 10^-2

Answer: 2. 1.2 × 10^-2

Question 86. Two Young’s modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of :

1. 2: 1
2. 4: 1
3. 1: 1
4. 1: 2

Answer: 1. 2:1

Question 87. The bulk modulus of a spherical object is ’B’. If it is subjected to uniform pressure ‘p’, the fractional decrease in radius is:

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

Answer: 4. \(\frac{p}{3 B}\)

Question 88. Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

1. 9 F
2. F
3. 4 F
4. 6 F

Answer: 1. 9F

Question 89. A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to :

1. r³
2. r⁴
3. r⁵
4. r²

Answer: 3. r⁵

Question 90. When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+ l). The elastic potential energy stored in the extended wire is:

1. \(\frac{1}{2} \mathrm{MgL}\)
2. Mgl
3. MgL
4. \(\frac{1}{2} \mathrm{Mg} \ell\)

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

Question 91. Two small spherical metal balls, having equal masses, are made from materials of densitiesρ₁ and ρ₂ (_ρ1 = 8_ρ2) and have radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ₂. The ratio of their terminal velocities would be

1. \(\frac{79}{72}\)
2. \(\frac{19}{36}\)
3. \(\frac{39}{72}\)
4. \(\frac{79}{36}\)

Answer: 4. \(\frac{79}{36}\)

Question 92. A wire of length L, area of cross-section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young’s modulus is:

1. \(\frac{M g L}{A\left(L_1-L\right)}\)
2. \(\frac{M g L}{A L}\)
3. \(\frac{M g\left(L_1-L\right)}{A L}\)
4. \(\frac{M g L}{A L_1}\)

Question 93. Two wires are made of the same material and have the same volume. However, wire 1 has a cross-sectional area of A, and wire 2 has a cross-sectional area of 3A. If the length of wire 1 increases by Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?

1. 4F
2. 6F
3. 9F
4. F

Answer: 3. 9F

Question 94. If a ball of steel (density p = 7.8 g cm –3) attains a terminal velocity of 10 cm s-1 when falling in water (Coefficient of Viscosity η_water = 8.5 × 10^-4 Pa.s) then its terminal velocity in glycerine (p = 1.2 g cm^-3, η= 13.2 Pa.s.) would be, nearly :

1. 6.25 × 10^-4 cm s^-1
2. 6.45 × 10^-4 cm s^-1
3. 1.5 ×10^-5 cm s^-1
4. 1.6 ×10^-5 cm s^-1

Answer: 1. 6.25 × 10^-4 cm s^-1

Question 95. A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if the density and elasticity of steel are 7.7 × 10³ kg/m³ and 2.2 × 10¹¹ N/m² respectively?

1. 188.5 Hz
2. 178.2 Hz
3. 200.5 Hz
4. 770 Hz

Answer: 2. 178.2 Hz

Question 96. The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is : (For steel Young’s modulus is 2 × 10¹¹ N m^-2 and the coefficient of thermal expansion is 1.1 × 10^-5 K^-1)

1. 2.2 × 10⁸ Pa
2. 2.2 × 10⁹ Pa
3. 2.2 × 10⁷ Pa
4. 2.2 × 10⁶ Pa

Answer: 1. 2.2 × 108 Pa

Question 97. A pendulum suspended from a uniform wire of cross-sectional area A has period T. When an additional mass M is added to its bob, the period changes to TM. If Young’s modulus of the 1 material of the wire is Y then \(\frac{1}{\mathrm{Y}}\) is equal to : (g=gravitational acceleration)

1. \(\left[\left(\frac{T_M}{T}\right)^2-1\right] \frac{\mathrm{A}}{\mathrm{Mg}}\)
2. \(\left[\left(\frac{T_{\mathrm{M}}}{\mathrm{T}}\right)^2-1\right] \frac{\mathrm{Mg}}{\mathrm{A}}\)
3. \(\left[1-\left(\frac{T_M}{T}\right)^2\right] \frac{\mathrm{A}}{\mathrm{Mg}}\)
4. \(\left[1-\left(\frac{T}{T_M}\right)^2\right] \frac{\mathrm{A}}{\mathrm{Mg}}\)

Answer: 1. \(\left[\left(\frac{T_M}{T}\right)^2-1\right] \frac{\mathrm{A}}{\mathrm{Mg}}\)

Question 98. A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area floats on the surface of the liquid, covering the entire cross-section of the cylindrical container. When a mass m is placed on the surface of the piston to dr compress the liquid, the fractional decrement in the radius of the sphere, \(\left(\frac{d r}{r}\right)\) is

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

Answer: 1. \(\frac{\mathrm{mg}}{3 \mathrm{Ka}}\)

Question 99. A rod, of length L at room temperature and uniform area of cross-section A, is made of a metal having a coefficient of linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, and prevents any change in the length of the rod, when its temperature rises by ΔT K. Young’s modulus, Y, for this metal is :

1. \(\frac{2 \mathrm{~F}}{\mathrm{~A} \alpha \Delta \mathrm{T}}\)
2. \(\frac{F}{A \alpha(\Delta T-273)}\)
3. \(\frac{F}{A \alpha \Delta T}\)
4. \(\frac{F}{2 \mathrm{~A} \alpha \Delta \mathrm{T}}\)

Answer: 3. \(\frac{F}{A \alpha \Delta T}\)

Question 100. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of an increase in the length of the steel wire is :

1. 3.0 mm
2. Zero
3. 5.0 mm
4. 4.0

Answer: 1. 3.0mm