Friction PYQs Set 5 (PDF)

Set 5 of 7 · Questions 121-150 of 182

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Mere Teacher · Previous Year Questions JEE Main Physics · Friction · Set 5 (Q121-150)
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121. $A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is x^{2} = ay. If the coefficient of friction is µ, the highest distance above the x-axis at which the particle will be in equilibrium is -$ (1) $µa$ (2) $µ^{2} a$ (3) $\frac{1}{4} µ^{2} a$ (4) $\frac{1}{2} µ a$ 122. $A large drum having radius R is spinning around its axis with angular velocity ω, as shown in figure. The minimum value of ω so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as μ, is:$ (1) $\frac{μg}{R}$ (2) $\frac{g}{2 μR}$ (3) $\frac{2 g}{μR}$ (4) $\frac{g}{μR}$ 123. $A block A of mass m_{1} rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m_{2} is suspended. The coefficient of kinetic friction between the block and the table is μ_{k} . When the block A is sliding on the table, the tension in the string is$ (1) $\frac{( m _{2} + μ _{k} m _{1} ) g}{( m _{1} + m _{2} )}$ (2) $\frac{( m _{2} - μ _{k} m _{1} ) g}{( m _{1} + m _{2} )}$ (3) $\frac{m _{1} m _{2} ( 1 + μ _{k} ) g}{( m _{1} + m _{2} )}$ (4) $\frac{m _{1} m _{2} ( 1 - μ _{k} ) g}{( m _{1} + m _{2} )}$ 124. $Block A of mass 2 kg is placed over block B of mass 8 kg . The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5 . Coefficient of friction between A and B is 0.4 . A horizontal force of 10 N is applied on block B. The force of friction between A and B is (g = 10 m s^{- 2})$ (1) $100 N$ (2) $40 N$ (3) $50 N$ (4) $zero$ 125. $When a body slides down on inclined plane with coefficient of friction μ, then its acceleration will be$ (1) $g (sin θ - μ cos θ)$ (2) $g (sin θ + μ sec θ)$ (3) $g (μ sin θ - cos θ)$ (4) $gμ (sin θ - cos θ)$ 126. $A body of mass 20 kg is moving on a rough horizontal plane. A block of mass 3 kg is connected to the 20 kg mass by a string of negligible mass through a smooth pulley as shown in the below figure. The tension in the string is 27 N . The coefficient of kinetic friction between the heavier mass and the surface is (g = 10 m / s^{2})$ (1) $0.025$ (2) $0.035$ (3) $0.35$ (4) $0.25$ 127. $Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in ms^{- 2} is : (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):$ (1) $3$ (2) $4$ (3) $2$ (4) $1.2$ 128. $A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is [NEET 2024]$ (1) $zero$ (2) $4 N$ (3) $6 N$ (4) $10 N$ 129. $The maximum value of the applied force F such that the block as shown in the arrangement does not move is (Acceleration due to gravity, g = 10 ms^{- 2})$ (1) $20 N$ (2) $15 N$ (3) $25 N$ (4) $10 N$ 130. $Two blocks A and B masses m_{A} = 1 kg and m_{B} = 3 kg are kepton the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : (Take g = 10 m / s^{2})$ (1) $8N$ (2) $16 N$ (3) $40 N$ (4) $12 N$ 131. $When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60º with horizontal, it can travel a distance x_{1} along the plane. But when the inclination is decreased to 30º and the same object is shot with the same velocity, it can travel x_{2} distance. Then x_{1} : x_{2} will be:$ (1) $1 : 23$ (2) $1 : 2$ (3) $2 : 1$ (4) $1 : 3$ 132. $Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure The tensions T_{1} and T_{2} in the string are respectively:$ (1) $40 N, 64 N$ (2) $60 N, 80 N$ (3) $88 N, 96 N$ (4) $80 N, 100 N$ 133. $A block of mass m is placed on a surface with a vertical cross section given by y = \frac{x ^{3}}{6} . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:$ (1) $\frac{1}{6} m$ (2) $\frac{2}{3} m$ (3) $\frac{1}{3} m$ (4) $\frac{1}{2} m$ 134. $A cubic block of mass m is sliding down on an inclined plane at 60^{\circ} with an acceleration of \frac{g}{2}, the value of coefficient of kinetic friction is$ (1) $\frac{3}{2}$ (2) $\frac{2}{3}$ (3) $1 - \frac{3}{2}$ (4) $3 - 1$ 135. $In the figure the block of mass M is at rest on the floor. The acceleration with which a monkey of mass m should climb up along the rope of negligible mass so as to lift the block from the floor is,$ (1) $= (\frac{M}{m} - 1) g$ (2) $> (\frac{M}{m} - 1) g$ (3) $\frac{M}{m} g$ (4) $> \frac{M}{m} g$ 136. $A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60^{\circ} by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is : (g = 10 m / s^{2})$ (1) $53 J$ (2) $5 J$ (3) $5 \times 10^{3} J$ (4) $10 J$ 137. $A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is µ. The acceleration α of the cart that will prevent the block from falling satisfies$ (1) $α > \frac{m g}{μ}$ (2) $α > \frac{g}{μ m}$ (3) $α \geq \frac{g}{μ}$ (4) $α < \frac{g}{μ}$ 138. $A system consists of three masses m_{1}, m_{2} and m_{3} connected by a string passing over a pulley P . The mass m_{3} hangs freely and m_{2} and m_{1} are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m_{1} is: (Assume m_{1} = m_{2} = m_{3} = m)$ (1) $\frac{g ( 1 - g μ )}{9}$ (2) $\frac{2 g μ}{3}$ (3) $\frac{g ( 1 - 2 μ )}{3}$ (4) $\frac{g ( 1 - 2 μ )}{2}$ 139. $A block B is pushed momentarily along a horizontal surface with an initial velocity V. If μ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time$ (1) $gμ / V$ (2) $g/V$ (3) $V/g$ (4) $V / (g μ) .$ 140. $A motor vehicle of mass 1000 kg is moving on a circular road having banking angle 30^{\circ} and coefficient of friction 0.2 . Then the normal reaction force on the motor vehicle is about (Acceleration due to gravity = 10 ms^{- 2})$ (1) $6750 N$ (2) $9060 N$ (3) $1070 N$ (4) $13055 N$ 141. $A block of mass slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m=8kg, M=16kg. Assume all the surfaces shown in the figure to be frictionless.$ (1) $\frac{4}{3} g$ (2) $\frac{6}{5} g$ (3) $\frac{3}{5} g$ (4) $\frac{2}{3} g$ 142. $A body of mass 2 kg is on an inclined plane of inclination 30^{\circ} and coefficient of friction is (\frac{1}{3}) . The minimum force required to move the body up the inclined plane is (Acceleration due to gravity = 10 ms^{- 2})$ (1) $5.77 N$ (2) $10 N$ (3) $20 N$ (4) $15 N$ 143. $Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (Assume system in equilibrium):$ (1) $100N$ (2) $80N$ (3) $120N$ (4) $150N$ 144. $A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is: (Take g = 10 m/ s^{2})$ (1) $\frac{3}{4}$ (2) $\frac{1}{2}$ (3) $\frac{3}{2}$ (4) $\frac{2}{3}$ 145. $Maximum acceleration of the train in which a 50 kg box lying on its floor will remain stationary (Given : Co-efficient of static friction between the box and the train's floor is 0.3 and g = 10 m s^{- 2})$ (1) $5.0 m s^{- 2}$ (2) $3.0 m s^{- 2}$ (3) $1.5 m s^{- 2}$ (4) $15 m s^{- 2}$ 146. $A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity ω . The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ . The beaker will revolve with the disc if:$ (1) $R \leq \frac{μg}{2 ω ^{2}}$ (2) $R \leq \frac{μg}{ω ^{2}}$ (3) $R \geq \frac{μg}{2 ω ^{2}}$ (4) $R \geq \frac{μg}{ω ^{2}}$ 147. $A body of mass 1Kg rests on a horizontal floor with which it has a coefficient of static friction \frac{1}{3} . It is desired to make the body move by applying the minimum possible force FN. The value of F will be (Round off to the Nearest Integer) [Take (g = 10 ms^{- 2})$ 148. $A disc is kept on a smooth horizontal plane with its plane parallel to horizontal plane. A groove is made in the disc as shown in the figure. The coefficient of friction between mass m and surface of the groove is 2/5 and sin θ = 3/5. Find the acceleration of mass with respect to the frame of reference of the disc.$ 149. $A curved in a level road has a radius 75m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be__m/s.$ 150. $Three blocks M_{1}, M_{2}, M_{3} having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope 1, T_{1} when they are moving upward with acceleration of 2 ms^{- 2} is ___ N (if g = 10 m / s^{2}).$