NEET Physics Class 11 Chapter 6 Friction Multiple Choice Question And Answers

Friction Multiple Choice Question And Answers

Question 1. If the normal force is doubled, the coefficient of friction is:

1. Halved
2. Doubled
3. Tripled
4. Not changed

Answer: 4. Halved

Question 2. If the coefficient of friction of a plane inclined at 45º is 0.5, then the acceleration of a body sliding freely on it is (g = 9.8m/s²)-

1. 4.9 m/s²
2. 9.8 m/s²
3. \(\frac{9.8}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^2\)
4. \(\frac{9.8}{2 \sqrt{2}} \mathrm{~m} / \mathrm{s}^2 \)

Answer: 4. \(\frac{9.8}{2 \sqrt{2}} \mathrm{~m} / \mathrm{s}^2 \)

Question 3. A body of mass 100 g is sliding downward from an inclined plane of inclination 30°. What is the frictional force experienced if µ = 1.7 –

1. \(1.7 \times \sqrt{2} \times \frac{1}{\sqrt{3}} \mathrm{~N}\)
2. \(1.7 \times \sqrt{3} \times \frac{1}{2} \mathrm{~N}\)
3. \(1.7 \times \sqrt{3} \mathrm{~N}\)
4. \(1.7 \times \sqrt{2} \times \frac{1}{3} \mathrm{~N}\)

Answer: 2. \(1.7 \times \sqrt{3} \times \frac{1}{2} \mathrm{~N}\)

Question 4. A car is moving along a straight horizontal road with a speed v₀. If the coefficient of friction between the tyres and the road is µ then the shortest distance in which the car can be stopped is-

1. \(\frac{v_0^2}{2 \mu \mathrm{g}}\)
2. \(\frac{v_0}{\mu g}\)
3. \(\left(\frac{v_0}{\mu g}\right)^2\)
4. \(\frac{1}{\sqrt{3}}\)

Answer: 1. \(\frac{v_0^2}{2 \mu \mathrm{g}}\)

Question 5. A block of mass 10 kg is moving up an inclined plane of inclination 30° with an initial speed of 5 m/s. It stops after 0.5 s, what is the value of the coefficient of kinetic friction?

1. 0.5
2. 0.6 cm
3. \(\sqrt{3}\)
4. \(\frac{1}{\sqrt{3}}\)

Answer: 4. \(\frac{1}{\sqrt{3}}\)

Question 6. A particle is projected along a rough plane inclined at an angle of 45° with the horizontal if the \(\frac{1}{2}\) coefficient of friction is g

1. \(\frac{\mathrm{g}}{\sqrt{2}}\)
2. \(\frac{\mathrm{g}}{2}\)
3. \(\frac{g}{\sqrt{2}}\left(1+\frac{1}{2}\right)\)
4. \(\frac{g}{\sqrt{2}}\left(1-\frac{1}{2}\right)\)
5. Answer: 3. \(\frac{g}{\sqrt{2}}\left(1+\frac{1}{2}\right)\)

Question 7. A body of mass 10 kg lies on a rough horizontal surface. When a horizontal force of F newtons acts on it, it gets an acceleration of 5 m/s². And when the horizontal force is doubled, it gets an acceleration of 18 m/s². The coefficient of friction between the body and the horizontal surface is- (Take g = 10 m/s²)

1. 0.2
2. 0.4
3. 0.6
4. 0.8

Answer: 4. 0.8

Question 8. On the horizontal surface of a truck, a block of mass 1kg is placed (μ = 0.6) and the truck is moving with acceleration 5 m/sec², then frictional force on the block will be –

1. 5 N
2. 6 N
3. 5.88 N
4. 8 N

Answer: 1. 5 N

Question 9. A 10 kg box is placed on a surface. The coefficient of friction between the surface and box is μ = 0.5. If horizontal force 100 N is applied acceleration of the box will be (g = 10 m/sec²) –

1. 2.5 m/s²
2. 5 m/s²
3. 7.5 m/s²
4. None

Answer: 2. 5 m/s²

Question 10. A block B is pushed momentarily along a horizontal surface with an initial velocity v. If μ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time:

1. \(\frac{v}{g \mu}\)
2. \(\frac{g \mu}{v}\)
3. \(\frac{g}{v}\)
4. \(\frac{v}{g}\)

Answer: 1. \(\frac{v}{g \mu}\)

Question 11. A block of mass 5 kg is placed on a horizontal surface and a pushing force of 20 N is acting on the back as shown in the figure. If the coefficient of friction between the block and surface is 0.2, then calculate the frictional force and speed of the block after 15 seconds. (Given g = 10 m/s²)

1. 2.936 MS^-1
2. 4.936 MS^-1
3. 3.936 MS^-1
4. None of these

Answer: 3. 3.936 MS^-1

Question 12. A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then the coefficient of friction is :

1. 0.02
2. 0.03
3. 0.06
4. 0.01

Answer: 3. 0.06

Question 13. Consider a car moving on a straight road with a speed of 100 m/s. The distance at which the car can be stopped is (µ_k= 0.5)

1. 100 m
2. 400 m
3. 800 m
4. 1000 m

Answer: 4. 1000 m

Question 14. Starting from rest a body slides down a 45º inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is:

1. 0.75
2. 0.33
3. 0.25
4. 0.80

Answer: 1. 0.75

Question 15. A wooden block of mass m resting on a rough horizontal table (coefficient of friction = μ) is pulled by a force F as shown in the figure. The acceleration of the block moving horizontally is :

1. \(\frac{F \cos \theta}{m}\)
2. \(\frac{\mu F \sin \theta}{M}\)
3. \(\frac{F}{m}(\cos \theta+\mu \sin \theta)-\mu g\)
4. None

Answer: 3. \(\frac{F}{m}(\cos \theta+\mu \sin \theta)-\mu g\)

Question 16. A block of mass M = 5 kg is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force F = 40 N is applied, the acceleration of the block will be (g = 10 m/s²) :

1. 5.73 m/sec²
2. 8.0 m/sec²
3. 3.17 m/sec²
4. 10.0 m/sec²

Answer: 1. 5.73 m/sec²

Question 17. A body is projected up a rough inclined plane from the bottom with some velocity. It travels up the incline and then returns back. If the time of ascent is and time of descent is td, then

1. t_a= t_d
2. t_a> t_d
3. t_a< t_d
4. Data insufficient

Answer: 3. t_a< t_d

Question 18. The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom of the coefficient of friction for the lower half is given by

1. 2 tan φ
2. tan φ
3. 2 sin φ
4. 2 cos φ

Answer: 1. 2 tan φ

Question 19. The frictional force is –

1. Self-adjustable
2. Not self-adjustable
3. scalar quantity
4. Equal to the limiting force

Answer: 1. Self-adjustable

Question 20. A block is placed on a rough floor and a horizontal force F is applied to it. The force of friction f by the floor on the block is measured for different values of F and a graph is plotted between them-

1. The graph is a straight line of slope 45°
2. The graph is a straight line parallel to the F-axis
3. The graph is a straight line of slope 45° for small F and a straight line parallel to the F-axis for large F.
4. There is a small kink on the graph

1. 3, 4
2. 1, 4
3. 1, 2
4. 1, 3

Answer: 1. 3, 4

Question 21. A block A kept on an inclined surface just begins to slide if the inclination is 30°. The block is replaced by another block B and it is found that it just begins to slide if the inclination is 40° –

1. Mass of A > mass of B
2. Mass of A < mass of B
3. Mass of A = mass of B
4. All three are possible

Answer: 4. All the three are possible

Question 22. It is easier to pull a body than to push, because-

1. The coefficient of friction is more in pushing than in pulling
2. The friction force is more in pushing than in pulling
3. The body does not move forward when pushed.
4. None of these

Answer: 2. The friction force is more in pushing than that in pulling

Question 23. The coefficient of static friction between two surfaces depends on –

1. Nature of surfaces
2. The shape of the surfaces in contact
3. The area of contact
4. All of the above

Answer: 1. Nature of surfaces

Question 24. A box is lying on an inclined plane. If the box starts sliding when the angle of inclination is 60°, then the coefficient of static friction of the box and plane is-

1. 2.732
2. 1.732
3. 0.267
4. 0.176

Answer: 2. 1.732

Question 25. A 20 kg block is initially at rest. A 75 N force is required to set the block in motion. After the motion, a force of 60 N is applied to keep the block moving at a constant speed. The coefficient of static friction is-

1. 0.6
2. 0.52
3. 0.44
4. 0.35

Answer: 4. 0.35

Question 26. A block of metal is lying on the floor of a bus. The maximum acceleration which can be given to the bus so that the block may remain at rest will be

1. µg
2. \(\frac{\mu}{g}\)
3. µ²g
4. µg²

Answer: 1. µg

Question 27. A box ‘A’ is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time ‘t’, it decelerates. Then the reaction R by the floor on the box is given best by :

Answer: 3

Question 28. A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of frictional force acting on the block is (g = 9.8m/s²)

1. 2.5 N
2. 0.98 N
3. 4.9 N
4. 0.49 N

Answer: 2. 0.98 N

Question 29. A block of mass 2 kg rests on a rough inclined plane making an angle of 300 with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is (g = 9.8m/s²) :

1. 9.8 N
2. 0.7 × 9.8 N
3. 9.8 × 7 N
4. 0.8 × 9.8 N

Answer: 1. 9.8 N

Question 30. A block of mass 5 kg and surface area 2 m² just begins to slide down on an inclined plane when the angle of inclination is 30º. Keeping the mass the same, the surface area of the block is doubled. The angle at which it starts sliding down is :

1. 30º
2. 60º
3. 15º
4. None

Answer: 1. 30º

Question 31. A 60 kg body is pushed horizontally with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is (g = 10m/s²) :

1. 6 m/s²
2. 4.9 m/s²
3. 3.92 m/s²
4. 1 m/s²

Answer: 4. 1 m/s²

Question 32. The blocks A and B are arranged as shown in the figure. The pulley is frictionless. The mass of A is 10 kg. The coefficient of friction between block A and the horizontal surface is 0.20. The minimum mass of B to start the motion will be

1. 2 kg
2. 0.2 kg
3. 5 kg
4. 10 kg

Answer: 1. 2 kg

Question 33. In the case of a horse pulling a cart, the force that causes the horse to move forward is the force that :

1. The horse exerts on the ground
2. The horse exerts on the cart
3. The ground exerts on the horse
4. The cart exerts on the horse

Answer: 3. The ground exerts on the horse

Question 34. A uniform rope of length l lies on a table. If the coefficient of friction is μ then the maximum length I₁ of the part of this rope which can overhang from the edge of the table without sliding down is

1. \(\frac{\ell}{\mu}\)
2. \(\frac{\ell}{\mu+1}\)
3. \(\frac{\mu \ell}{1+\mu}\)
4. \(\frac{\mu \ell}{1-\mu}\)

Answer: 3. \(\frac{\mu \ell}{1+\mu}\)

Question 35. Block A of mass 4 kg and block B of mass 6 kg are resting on a horizontal surface as shown in the figure. There is no friction between the block B and the horizontal surface. The coefficient of friction between the blocks is 0.2. If the value of g = 10 ms^-2, the maximum horizontal force F that can be applied on block B without any relative motion between A and B is

1. 20 N
2. 40 N
3. 60 N
4. 100 N

Answer: 1. 20 N

Question 36. Consider the situation. The wall is smooth but the surfaces of A and B in contact are rough. The friction on B due to A in equilibrium-

1. Is upward
2. Is downward
3. Is zero
4. The system cannot remain in equilibrium

Answer: 4. The system cannot remain in equilibrium

Question 37. Suppose all the surfaces in the previous problem are rough. The direction of friction on B due to A-

1. Is upward
2. Is downward
3. Is zero
4. Depends on the masses of A and B

Answer: 1. Is upward

Question 38. A body of mass M is kept on a rough horizontal surface (friction coefficient = µ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F where-

1. F = Mg
2. F = µMg
3. \(M g \leq F \leq M g \sqrt{1+\mu^2}\)
4. \(M g \geq F \geq M g \sqrt{1+\mu^2}\)

Answer: 3. \(M g \leq F \leq M g \sqrt{1+\mu^2}\)

Question 39. In a situation where the contact force by a rough horizontal surface on a body placed on it has constant magnitude if the angle between this force and the vertical is decreased the frictional force between the surface and the body will-

1. Increase
2. Decrease
3. Remain the same
4. May increase or decrease

Answer: 2. Decrease

Question 40. An inclined plane is inclined at an angle θ with the horizontal. A body of mass m rests on it, if the coefficient of friction is µ, then the minimum force that has to be applied to the inclined plane to make the body just move up the inclined plane is-

1. mgsinθ
2. µmgcosθ
3. µmgcosθ – mgsinθ
4. µmgcosθ + mgsinθ

Answer: 4. µmgcosθ + mgsinθ

Question 41. A block W is held against a vertical wall by applying a horizontal force F. The minimum value of F needed to hold the block is if μ < 1

1. Less than W
2. Equal to W
3. Greater than W
4. Data is insufficient

Answer: 3. Greater than W

Question 42. The system shown in the figure is in equilibrium. The maximum value of W, so that the maximum value of static frictional force on 100 kg body is 450 N, will be:-

1. 100 N
2. 250 N
3. 450 N
4. 1000 N

Answer: 3. 450 N

Question 43. A block of mass 20 kg is kept on a rough incline plane. If the angle of repose is 30°, then what should be the value of F_ext so that the block does not move over the inclined plane?

1. 120 N
2. 200 N
3. 110 N
4. Both 1 and 2

Answer: 4. Both 1 and 2

Question 44. What is the maximum value of the force F such that the block shown in the arrangement, does not move :

1. 20 N
2. 10 N
3. 12 N
4. 15 N

Answer: 1. 20 N

Question 45. The coefficient of static friction, μs, between block A of mass 2kg and the table as shown in the figure, is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless : (g = 10 m/s²)

1. 2.0 kg
2. 4.0 kg
3. 0.2 kg
4. 0.4 kg

Answer: 4. 0.4 kg

Question 46. A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is :

1. 2 kg
2. 50 N
3. 100 N
4. 2 N

Answer: 4. 2 N

Question 47. A block rests on a rough inclined plane making an angle of 30º with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take g = 10 m/s²) :

1. 2.0
2. 4.0
3. 1.6
4. 2.5

Answer: 1. 2.0

Question 48. A block of mass 20 kg is acted upon by a force F = 30 N at an angle of 53° with the horizontal in a downward direction as shown. The coefficient of friction between the block and the horizontal surface is 0.2. The friction force acting on the block by the ground is (g = 10 m/s²)

1. 40.0 N
2. 30.0 N
3. 18.0 N
4. 44.8 N

Answer: 3. 18.0 N

Question 49. A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle θ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is:-

1. \(\frac{P+Q \sin \theta}{m g+Q \cos \theta}\)
2. \(\frac{P \cos \theta+Q}{m g-Q \sin \theta}\)
3. \(\frac{P+Q \cos \theta}{m g+Q \sin \theta}\)
4. \(\frac{P \sin \theta+Q}{m g-Q \cos \theta}\)

Answer: 1. \(\frac{P+Q \sin \theta}{m g+Q \cos \theta}\)

Question 50. In the arrangement shown in the figure, a 5 kg block is placed on a rough table (μ =0.4) and a 3kg mass is connected at one end. then the range of mass m, for which the system will remain in equilibrium is

1. 1 kg to 3 kg
2. 1 kg to 5 kg
3. Any value greater than 8 kg
4. 3 kg to 5 kg

Answer: 2. 1 kg to 5 kg

Question 51. Two masses A and B of 10 kg and 5 kg respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of A with table is 0.2. The minimum mass of C that may be placed on A to prevent it from moving is

1. 15 kg
2. 10 kg
3. 5 kg
4. 12 kg

Answer: 1. 15 kg

Question 52. A block of mass m is at rest relative to the stationary wedge of mass M. The coefficient of friction between block and wedge is µ. The wedge is now pulled horizontally with acceleration ‘a’ as shown in the figure. Then the minimum magnitude of ‘a’ for the friction between block and wedge to be zero is :

1. g tan θ
2. µ g tan θ
3. g cot θ
4. µ g cot θ

Answer: 3. g cot θ

Question 53. A uniform rope of length l lies on a table. If the coefficient of friction is
μ, then the maximum length l₁ of the part of this rope which can overhang from the edge of the table without sliding down is

1. \(\frac{l}{\mu}\)
2. \(\frac{l}{\mu+l}\)
3. \(\frac{\mu l}{1+\mu}\)
4. \(\frac{\mu l}{\mu-1}\)

Answer: 3. \(\frac{\mu l}{1+\mu}\)

Question 54. A heavy uniform chain lies on a horizontal tabletop. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of the length of the chain, that can hang over one edge of the table is

1. 20%
2. 25%
3. 35%
4. 15%

Answer: 1. 20%

Question 55. A uniform chain of length L changes partly from a table which is kept in equilibrium by friction. The maximum length that can withstand without slipping is l, and then the coefficient of friction between the table and the chain is

1. \(\frac{l}{L}\)
2. \(\frac{l}{L+l}\)
3. \(\frac{l}{L-1}\)
4. \(\frac{L}{L+l}\)

Answer: 3. \(\frac{l}{L-1}\)

Question 56. A uniform metal chain is placed on a rough table such that one end of the chain hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is

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

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

Question 57. A rope lies on a table such that part of it lays over. The rope begins to slide when the length of the hanging part is 25 % of the entire length. The coefficient of friction between the rope and the table is:

1. 0.33
2. 0.25
3. 0.5
4. 0.2

Answer: 1. 0.33

Question 58. Two blocks A and B placed on a plane surface as shown in the figure. The mass of block A is 100 kg and that of block B is 200 kg. Block A is tied to a stand and block B is pulled by a force F. If the coefficient of friction between the surfaces of A and B is 0.2 and the coefficient of friction between B and the plane is 0.3 then for the motion of B the minimum value of F will be

1. 700 N
2. 1050 N
3. 900 N
4. 1100 N

Answer: 4. 1100N

Question 59. A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic coefficient is 0.40. The 10 kg block is acted upon by a horizontal force of 100N. If g = 9.8 m/s², the resulting acceleration of the slab will be

1. 0.98 m/s²
2. 1.47 m/s²
3. 1.52 m/s²
4. 6.1 m/s²

Answer: 1. 0.98 m/s²

Question 60. A body A of mass 1kg rests on a smooth surface. Another body B of mass 0.2 kg is placed over A as shown. The coefficient of static friction between A and B is 0.15. B will bring to slide on A if a pulled with a force greater than-

1. 1.764 N
2. 0.1764 N
3. 0.3 N
4. It will not slide for any F

Answer: 1. 1.764 N

Question 61. A ramp is constructed with a parabolic shape such that the height y at any point on its surface is given in terms of its horizontal distance x from the bottom of the ramp (x = y = 0) by y =. A small block is to be set on the ramp. The maximum height from the bottom level at which the block can be kept on the ramp without sliding is (Given that μ_s= 0.5)

1. 2.5 m
2. 5 m
3. 1.25 m
4. 2.75 m

Answer: 3. 1.25 m

Question 62. Two blocks A and B of equal masses are sliding down along straight parallel lines on an inclined plane of 45°. Their coefficients of kinetic friction are μ_A= 0.2 and μ_B= 0.3 respectively. At t = 0, both the blocks are at rest and block A is \(\sqrt{2}\) 2 meters behind block B. The time and distance from the initial position where the front faces of the blocks come in line on the inclined plane as shown in the figure. (Use g = 10 ms^-2.)

1. \(2 \mathrm{~s}, 8 \sqrt{2} \mathrm{~m}\)
2. \(\sqrt{2} \mathrm{~s}, 7 \mathrm{~m}\)
3. \(\sqrt{2} \mathrm{~s}, 7 \sqrt{2} \mathrm{~m}\)
4. \(2 \mathrm{~s}, 7 / \sqrt{2} \mathrm{~m}\)

Answer: 1. \(2 \mathrm{~s}, 8 \sqrt{2} \mathrm{~m}\)

Question 63. A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tanθ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁= mg(sinθ – μcosθ) to P₂= mg(sinθ + μcosθ), the frictional force f versus P graph will look like :

Answer: 1

Question 64. A smooth block is released at rest on a 45º incline and then slides a distance d. The time taken to slide is n times as much to slide on a rough incline than on a smooth incline. The coefficient of friction is-

1. \(\mu_s=1-\frac{1}{n^2}\)
2. \(\mu_s=\sqrt{1-\frac{1}{n^2}}\)
3. \(\mu_k=1-\frac{1}{n^2}\)
4. \(\mu_k=\sqrt{1-\frac{1}{n^2}}\)

Answer: 3. \(\mu_k=1-\frac{1}{n^2}\)

Question 65. Two blocks m₁= 4kg and m₂= 2kg, are connected by a weightless rod on a plane having an inclination of 370. The coefficients of dynamic friction of m₁ and m₂ with the inclined plane are μ = 0.25. Then the common acceleration of the two blocks and the tension in the rod are:

1. 4 m/s², T = 0
2. 2 m/s², T = 5 N
3. 10 m/s²,T = 10 N
4. 15 m/s², T = 9N

Answer: 1. 4 m/s2, T = 0

Question 66. A force F = t is applied to block A as shown in the figure. The force is applied at t = 0 seconds when the system is at rest and the string is just straight without tension. Which of the following graphs gives the friction force between B and the horizontal surface as a function of time ‘t’?

Answer: 1

Question 67. If the coefficient of friction between A and B is μ, the maximum horizontal acceleration of the wedge A for which B will remain at rest w.r.t the wedge is :

1. μ g
2. \(g\left(\frac{1+\mu}{1-\mu}\right)\)
3. \(\frac{\mathrm{g}}{\mu}\)
4. \(g\left(\frac{1-\mu}{1+\mu}\right)\)

Answer: 2. \(g\left(\frac{1+\mu}{1-\mu}\right)\)

Question 68. What is the minimum stopping distance for a vehicle of mass m moving with speed v along a level road? If the coefficient of friction between the tyres and the road is μ.

1. \(\frac{v^2}{2 \mu \mathrm{g}}\)
2. \(\frac{2 v^2}{\mu \mathrm{g}}\)
3. \(\frac{v^2}{\mu g}\)
4. None of these

Answer: 1. \(\frac{v^2}{2 \mu \mathrm{g}}\)

Question 69. A block of mass m₁= 1 kg and another mass m₂= 2 kg, are placed together (see figure) on an inclined plane with angle of inclination θ. Various values of θ are given in List 1. The coefficient of friction between the block m₁ and the plane is always zero. The coefficient of static and dynamic friction between the block m₂ and the plane is equal to μ = 0.3. In List 2 expression for the friction on block m₂ is given. Match the correct expression of the friction in List II with the angles given in List 1, and choose the correct option. The acceleration due to gravity is denoted by g.

[Useful information : tan(5.5°) ≈ 0.1 ; tan (11.5°) ≈ 0.2 ; tan(16.5º ≈ 0.3)]

List-1

P. θ = 5°

Q. θ = 10°

R. θ = 15°

S. θ = 20°

List-2

1. m₂g sin θ

2. (m₁+ m₂)g sin θ

3. μm₂g cos θ

4. μ(m₁+ m₂)g cos θ

Code:

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

Answer: 4. P-2, Q-2, R-3,S-3

Question 70. A block of mass m is in contact with cart C as shown in the figure.

The coefficient of static friction between the block and the cart is μ. The acceleration α of the cart that will prevent the block from falling satisfies

1. \(\alpha>\frac{m g}{\mu}\)
2. \(\alpha>\frac{g}{\mu m}\)
3. \(\alpha \geq \frac{g}{\mu}\)
4. \(\alpha<\frac{g}{\mu}\)

Answer: 3. \(\alpha \geq \frac{g}{\mu}\)

Question 71. A conveyor belt is moving at a constant speed of 2m/s. A box is gently dropped on it. The coefficient of friction between them is µ= 0.5. The distance that the box will move relative to the belt before coming to rest on it taking g = 10 ms^-2, is :

1. 1.2 m
2. 0.6 m
3. Zero
4. 0.4 m

Answer: 4. 0.4 m

Question 72. A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ. The coin will revolve with the record if

1. \(\mathrm{r}=\mu \mathrm{g} \omega^2\)
2. \(r=\frac{\omega^2}{\mu g}\)
3. \(r \leq \frac{\mu g}{\omega^2}\)
4. \(r \geq \frac{\mu g}{\omega^2}\)

Answer: 3. \(r \leq \frac{\mu g}{\omega^2}\)

Question 73. A car of mass m is moving on a level circular track of radius R. If μ_s represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by :

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

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

Question 74. A system consists of three masses m₁, m₂ and m₃ connected by a string passing over a pulley P. The mass m₃ hangs freely and m₂ and m₁ are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m₁ is : (Assume m₁= m₂= m₃= m)

1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \(\frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)

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

Question 75. A Block A of mass m₁ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of a table and from its other end, another block B of mass m₂ is suspended. The coefficient of kinetic friction between the block and the table is μ_k. When the block A is sliding on the table, the tension in the string is :

1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \(\frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)

Answer: 2. \(\frac{2 g \mu}{3}\)

Question 76. A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30º the box starts to slip and slides 4.0 m down the plank in 4.0s. The coefficients of static and kinetic friction between the box and the plank will be, respectively :

1. 0.6 and 0.5
2. 0.5 and 0.6
3. 0.4 and 0.3
4. 0.6 and 0.6

Answer: 1. 0.6 and 0.5

Question 77. Which one of the following statements is incorrect?

1. Rolling friction is smaller than sliding friction.
2. The coefficient of sliding friction has dimensions of length.
3. Frictional force opposes the relative motion.
4. The limiting value of static friction is directly proportional to normal reaction.

Answer: 2. Coefficient of sliding friction has dimensions of length.

Question 78. The minimum force required to start pushing a body up a rough (frictional coefficient μ) inclined plane is F₁ while the minimum force needed to prevent it from sliding down is F₂. If the inclined plane makes an F angle θ from the horizontal such that tan θ = 2μ then the ratio \(\frac{F_1}{F_2}\) is :

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

Answer: 3. 3

Question 79. A block of mass m is placed on a surface with a vertical cross-section given by
y =\(\frac{x^3}{6}\). If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

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

Answer: 1. \(\frac{1}{6} m\)

Question 80. Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is:

1. 100N
2. 80N
3. 120N
4. 150N

Answer: 3. 120N

Question 81. Two masses m₁ = 5kg and m₂ = 10kg connected by an inextensible string over a frictionless pulley are moving as shown in the figure. The coefficient of friction of the horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is :

1. 43.3 kg
2. 10.3 kg
3. 18.3 kg
4. 27.3 kg

Answer: 4. 27.3 kg

Question 82. A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3N is applied to the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward (take g = 10 m/s²)

1. 32 N
2. 23 N
3. 25 N
4. 18 N

Answer: 1. 32 N

Question 83. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force of 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : (Take g = 10 m/s²)

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

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