Friction PYQs Set 3 (PDF)

Set 3 of 7 · Questions 61-90 of 182

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Mere Teacher · Previous Year Questions JEE Main Physics · Friction · Set 3 (Q61-90)
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61. $A board is balanced on a rough horizontal semicircular log. Equilibrium is obtained with the help of addition of a weight to one of the ends of the board when the board makes an angle θwith the horizontal. Coefficient of friction between the log and the board is$ (1) $tanθ$ (2) $cosθ$ (3) $cot$ (4) $sin$ 62. $A horizontal force just sufficient to move a body of mass 4 kg lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are. 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, g = 10 ms^{- 2}).$ (1) $6 ms^{- 2}$ (2) $8 ms^{- 2}$ (3) $2 ms^{- 2}$ (4) $4 ms^{- 2}$ 63. $A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by force F=20N, making an angle of 30° with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is μ = 0.2 . The difference between the accelerations of the block, in case (B) and case (A) will be:g=10 ms^{- 2}$ (1) $0.4 ms^{- 2}$ (2) $3.2 ms^{- 2}$ (3) $0.8 ms^{- 2}$ (4) $0 ms^{- 2}$ 64. $A block of mass 2 kg is pulled at a constant speed with a taut rope along a frictionless plane that is inclined at 30^{\circ} . Then the work done by the tension in the rope in pulling it a distance 4 m along the inclined plane in joule is (acceleration due to gravity = 10 ms^{- 2} .)$ (1) $40$ (2) $20$ (3) $68$ (4) $136$ 65. $A block of metal weighing 2 kg is resting on a Motionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 k g s^{- 1} and at a speed of 10 m s^{- 1} . Then, the initial acceleration of the block, in m s^{- 2}, will be:$ (1) $3$ (2) $6$ (3) $5$ (4) $4$ 66. $Two bodies of masses m_{1} = 5 kg and m_{2} = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass mi will be: [Take g= 10 m s^{- 2}]$ (1) $30N$ (2) $40N$ (3) $50 N$ (4) $60 N$ 67. $A mass m is attached to two springs as shown in figure. The spring constants of two springs are K_{1} and K_{2} . For the frictionless surface, the time period of oscillation of mass m is$ (1) $2 π \frac{m}{K _{1} + K _{2}}$ (2) $\frac{1}{2 π} \frac{K _{1} - K _{2}}{m}$ (3) $2 π \frac{m}{K _{1} - K _{2}}$ (4) $\frac{1}{2 π} \frac{K _{1} + K _{2}}{m}$ 68. $The minimum force required to start pushing a body up a rough (frictional coefficient μ) inclined plane is F_{1} while the minimum force needed to prevent it from sliding down is F_{2} . If the inclined plane makes an angle θ from the horizontal such that tan θ = 2 μ then the ratio \frac{F _{1}}{F _{2}} is:$ (1) $1$ (2) $2$ (3) $3$ (4) $4$ 69. $A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is. (Given g = 10 m s^{- 2} .)$ (1) $1 m s^{- 2}$ (2) $1/5 m s^{- 2}$ (3) $4/5 m s^{- 2}$ (4) $8/ 11 m s^{- 2}$ 70. $What is the maximum force F that can be applied on block m_{1}, so that both m_{1} and m_{2} will move together? There is no friction between m_{1} and the horizontal table. The coefficient of friction between m_{1} and m_{2} is μ$ (1) $μ m_{2} g$ (2) $μ (m_{1} + m_{2}) g$ (3) $μ \frac{m _{1} m _{2}}{( m _{1} + m _{2} )} g$ (4) $μ m_{1} g$ 71. $The minimum force required to start pushing a body up a rough (friction coefficient µ) inclined plane is F_{1} while the minimum force needed to prevent it from sliding down is F_{2} . If the inclined plane makes an angle θ from the horizontal such that tan θ= 2µ then the ratio \frac{F _{1}}{F _{2}} is$ (1) $1$ (2) $2$ (3) $3$ (4) $4$ 72. $A block 'A' takes 2 s to slide down a frictionless incline of 30° and length ’ l ’, kept inside a lift going up with uniform velocity ’ v ’ . If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately:$ (1) $2.66s$ (2) $0.83s$ (3) $1.68s$ (4) $0.70s$ 73. $An insect is at the bottom of a hemispherical ditch of radius 1 m . It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is (g = 10 m s^{- 2})$ (1) $0.45 m$ (2) $0.80 m$ (3) $0.20 m$ (4) $0.60 m$ 74. $Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is$ (1) $100N$ (2) $80N$ (3) $120N$ (4) $150N$ 75. $A car of mass m is moving on a level circular track of radius R . If μ_{s} represents the static friction between the road and tires of the car, the maximum speed of the car in circular motion is given by$ (1) $μ_{s} mRg$ (2) $\frac{Rg}{μ _{s}}$ (3) $\frac{mRg}{μ _{s}}$ (4) $μ_{s} Rg$ 76. $A block of mass 10 kg is kept on a rough inclined plane inclined plane as shown in the figure. A force of 3N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms^{- 2})$ (1) $32 N$ (2) $18 N$ (3) $23 N$ (4) $25 N$ 77. $If 100 N force is applied to 10 kg block as shown in the diagram, the acceleration of 40 kg slab is$ (1) $1.65 ms^{- 2}$ (2) $0.98 ms^{- 2}$ (3) $0.5 ms^{- 2}$ (4) $0.25 ms^{- 2}$ 78. $A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m / s^{2}) [NEET 2019]$ (1) $\frac{10}{2 π} rad / s$ (2) $10 rad / s$ (3) $10 π rad / s$ (4) $10 rad / s$ 79. $A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air (f_{a}) cannot be ignored, the forces acting on the ball at the position X are represented by$ (1) (2) (3) (4) 80. $A block of mass m is on inclined plane of angle θ. The coefficient of friction between the block and the plane is µ and tan θ > µ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P_{1} = mg (sin θ - µcos θ) to P_{2} = mg (sin θ + µcos θ), the frictional force f versus P graph will look like:$ (1) (2) (3) (4) 81. $A block of mass 2 kg moving on a horizontal surface with speed of 4 m s^{- 1} enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = -kx where k = 12 N m^{- 1} . The speed of the block as it just crosses the rough surface will be:$ (1) $Zero$ (2) $1. 5 m s^{- 1}$ (3) $2. 0 m s^{- 1}$ (4) $2. 5 m s^{- 1}$ 82. $A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is$ (1) $20%$ (2) $25%$ (3) $35%$ (4) $15%$ 83. $A light string passing over a smooth light fixed pulley connects two blocks of masses m_{1} and m_{2} . If the acceleration of the system is g /8, then the ratio of masses is$ (1) $\frac{9}{7}$ (2) $\frac{8}{1}$ (3) $\frac{4}{3}$ (4) $\frac{5}{3}$ 84. $A block of mass m is in contact with the cart C as shown in the figure. The Coefficient of static friction between the block and the cart is μ . The acceleration α of the cart that will prevent the block from falling satisfies$ (1) $α > \frac{m g}{μ}$ (2) $α > \frac{g}{μ m}$ (3) $α \geq \frac{g}{μ}$ (4) $α < \frac{g}{μ}$ 85. $A car is moving along a circular path having coefficient of friction 0.5 and radius of curvature 16.2 m . Then the maximum velocity of the car that can travel without falling outwards is (Acceleration due to gravity = 10 ms^{- 2})$ (1) $18 ms^{- 1}$ (2) $32.4 kmh^{- 1}$ (3) $18 kmh^{- 1}$ (4) $32.4 ms^{- 1}$ 86. $A block A of mass m_{1} rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m_{2} is suspended. The coefficient of kinetic friction between the block and the table is µ_{k} . When the block A is sliding on the table, the tension in the string is:$ (1) $\frac{( m _{2} - μ k m _{1} ) g}{( m _{1} + m _{2} )}$ (2) $\frac{m _{1} m _{2} ( 1 + μ _{k} ) g}{( m _{1} + m _{2} )}$ (3) $\frac{m _{1} m _{2} ( 1 - μ _{k} ) g}{( m _{1} + m _{2} )}$ (4) $\frac{( m _{2} + μ _{k} m _{1} ) g}{( m _{1} + m _{2} )}$ 87. $A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ . If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :$ (1) $\frac{μg}{r}$ (2) $\frac{r}{μg}$ (3) $\frac{μg}{r}$ (4) $\frac{μ}{rg}$ 88. $A bullet from a gun is fired on a rectangular wooden block with velocity u . When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u /3 . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is [NEET 2023]$ (1) $24 cm$ (2) $28 cm$ (3) $30 cm$ (4) $27 cm$ 89. $An inclined plane is bent in such a way that the vertical cross-section is given by y = \frac{x ^{2}}{4} where y is in verticaland x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ = 0.5, the maximum height in cm at which a stationary block will not slip downward is___.$ 90. $A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is µ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define k = 10 µ, then value of k is$