Friction PYQs Set 4 (PDF)

Set 4 of 7 · Questions 91-120 of 182

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Mere Teacher · Previous Year Questions JEE Main Physics · Friction · Set 4 (Q91-120)
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91. $A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:$ (1) $20 m s^{- 1}$ (2) $40 m s^{- 1}$ (3) $400 m s^{- 1}$ (4) $10 m s^{- 1}$ 92. $A man tries to remain in steady state by pushing his feet and hands against two parallel walls. Then for equilibrium$ (1) $Force of friction should be equal on the two walls.$ (2) $Force exerted by him on both walls should be equal and the walls should not be frictionless.$ (3) $He should press his feet with greater force.$ (4) $Coefficient of friction should be equal for both walls.$ 93. $A constant horizontal force F of magnitude 10 N is applied to a block A and this produces an acceleration of magnitude 20 m / s^{2} . If this block A is then kept against another block B of mass 1.5 kg as shown in figure and a force F^{’} of 20 N is applied, find the force on the block B . Neglect friction.$ (1) $15 N$ (2) $10 N$ (3) $20 N$ (4) $5 N$ 94. $A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 3 0^{o}, the box starts to slip and slides 4.0 m down the plank in 4.0 s . The coefficients of static and kinetic friction between the box and the plank will be, respectively$ (1) $0.5 and 0.6$ (2) $0.4 and 0.3$ (3) $0.6 and 0.6$ (4) $0.6 and 0.5$ 95. $A system consists of three masses m_{1}, m_{2} and m_{3} connected by a string passing over a pulley P. The mass m_{l} hangs freely and m_{2} and m_{3} are on a rough horizontal table (the coefficient of friction = μ) . The pulley is frictionless and of negligible mass. The downward acceleration of mass m_{1} is (Assume m_{1} = m_{2} = m_{3} = m)$ (1) $\frac{g ( 1 - gμ )}{9}$ (2) $\frac{2 g μ}{3}$ (3) $\frac{g ( 1 - 2 μ )}{3}$ (4) $\frac{g ( 1 - 2 μ )}{2}$ 96. $A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t . Which of the following curve best describes acceleration of the block with time:$ (1) (2) (3) (4) 97. $Two blocks of masses ' M' and ' m' are placed on one another on a smooth horizontal surface as shown in the figure. The force ' F' is acting on the mass ' M' horizontally during time interval ' t'. Assuming no relative sliding between the blocks, the work done by friction on the blocks is \dots \dots$ (1) $\frac{Ft}{2 ( M + m )}$ (2) $\frac{M + m}{m t ^{2}}$ (3) $\frac{m F ^{2} t ^{2}}{2 ( M + m ) ^{2}}$ (4) $\frac{F ^{2} t ^{2}}{( M + m )}$ 98. $Two masses m_{1} = 5kg and m_{2} = 10kg connected by an inextensible string over a frictionless pulley are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m_{2} to stop the motion is:$ (1) $43.3 kg$ (2) $10.3 kg$ (3) $18.3 kg$ (4) $27.3 kg$ 99. $Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is$ (1) $2 N$ (2) $6 N$ (3) $8 N$ (4) $18 N$ 100. $A block of mass m is lying on a rough inclined plane having an inclination α = tan^{- 1} (\frac{1}{5}) . The inclined plane is moving horizontally with a constant acceleration of a = 2 ms^{- 2} as shown in the figure. The minimum value of coefficient of friction, so that the block remains stationary with respect to the inclined plane is (Take, g = 10 ms^{- 2})$ (1) $\frac{2}{9}$ (2) $\frac{5}{12}$ (3) $\frac{1}{5}$ (4) $\frac{2}{5}$ 101. $Three masses M = 100 kg, m_{1} = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 m s^{- 2} . The value of F is: (Take g= 10 m s^{- 2})$ (1) $3360 N$ (2) $3380N$ (3) $3120N$ (4) $3240N$ 102. $A block kept on a rough inclined plane, as shown in the in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is: [Take g = 10 m / s^{2}]$ (1) $\frac{3}{2}$ (2) $\frac{3}{4}$ (3) $\frac{1}{2}$ (4) $\frac{2}{3}$ 103. $Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (^{μ}) is equal to:$ (1) $0.33$ (2) $0.60$ (3) $0.25$ (4) $0.50$ 104. $Two fixed frictionless inclined planes making an angle 30º and 60º with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?$ (1) $4.9 ms-2 in horizontal direction$ (2) $9.8 ms-2 in vertical direction$ (3) $Zero$ (4) $4.9 m s^{- 2} in vertical direction$ 105. $Three blocks are connected by massless strings on a frictionless inclined plane of 30^{\circ} as shown in the figure. A force of 104 N is applied upward along the incline to mass m_{3} causing an upward motion of the blocks. What is the acceleration of the blocks? (Assume, acceleration due to gravity, g = 10 m / s^{2})$ (1) $6.0 m / s^{2}$ (2) $4.5 m / s^{2}$ (3) $3.0 m / s^{2}$ (4) $1.5 m / s^{2}$ 106. $In the arrangement shown in the figure, the coefficient of friction between two blocks is 0.5 . The force of friction between the two blocks is (Assume that the 4 kg block is placed on a smooth horizontal surface.) (Acceleration due to gravity = 10 ms^{- 2} .)$ (1) $8 N$ (2) $10 N$ (3) $6 N$ (4) $4 N$ 107. $A block kept on a rough surface starts sliding when the inclination of the surface is ' θ ' with respect to the horizontal. The coefficient of static friction between the block and the surface is$ (1) $sin θ$ (2) $tan θ$ (3) $cos θ$ (4) $sec θ$ 108. $Calculate the acceleration of the block and trolly system as shown in the figure. The coefficient of kinetic friction between the trolly and the surface is 0.05. (g = 10 m / s^{2}, mass of the string is negligible and no other friction exists). [NEET 2020]$ (1) $1.25 m / s^{2}$ (2) $1.50 m / s^{2}$ (3) $1.66 m / s^{2}$ (4) $1.00 m / s^{2}$ 109. $A body of mass m is kept on a rough horizontal surface (coefficient of friction = μ). Horizontal force is applied on the body but it does not move. The resultant of normal reaction and the frictional force acting on the object is given F, where F is [NEET 2019]$ (1) $\| F \| = mg + μmg$ (2) $\| F \| = μmg$ (3) $∣ F ∣ \leq mg 1 + μ^{2}$ (4) $\| F \| = mg$ 110. $A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle θ with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 m/ s^{2})$ (1) $θ = 45°$ (2) $θ > 45° and a frictional force acts on the block towards P.$ (3) $θ > 45° and a frictional force acts on the block towards Q.$ (4) $θ < 45° and a frictional force acts on the block towards Q.$ 111. $Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between block and table is 0.1 . Find the force F, that must be given to the 0.8 kg block such that it attains accelerations of 5 m / s^{2} . (Assume, acceleration due to gravity, g = 10 m / s^{2} .)$ (1) $6.4 N$ (2) $7.1 N$ (3) $6.0 N$ (4) $7.8 N$ 112. $As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30°, with horizontal. For μ_{s} = 0.25, the block will just start to move for the value of F: [Given g = 10 m s^{- 2}]$ (1) $33.3N$ (2) $25.2 N$ (3) $20N$ (4) $35.7 N$ 113. $A system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system is in equilibrium then the value of m is$ (1) $1 kg$ (2) $0.5 kg$ (3) $0.75 kg$ (4) $0.25 kg$ 114. $A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30^{\circ}, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients or static and kinetic friction between the box and the plank will be, respectively$ (1) $0.6 and 0.6$ (2) $0.6 and 0.5$ (3) $0.5 and 0.6$ (4) $0.4 and 0.3$ 115. $An object requires 500 N force to be pulled up on a 30^{\circ} frictionless smooth inclined plane at a constant speed. The weight of the object is$ (1) $5002 N$ (2) $1000 N$ (3) $10002 N$ (4) $5003 N$ 116. $A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is μ_{s}, then the magnitude of negative lift F_{L} acting downwards on the car is: (Assume forces on the four tyres are identical and g = acceleration due to gravity)$ (1) $m (\frac{v ^{2}}{μ _{s} R} + g)$ (2) $m (\frac{v ^{2}}{μ _{8} R} - g)$ (3) $m (g - \frac{v ^{2}}{μ _{s} R})$ (4) $- m (g + \frac{v ^{2}}{μ _{s} R})$ 117. $A body is made to move up along an inclined plane of inclination 30^{\circ} and the coefficient of friction is 0.5 , then its retardation is (g - acceleration due to gravity)$ (1) $(\frac{2 + 3}{4}) g$ (2) $(\frac{2 - 3}{4}) g$ (3) $(\frac{2 - 3}{2}) g$ (4) $(\frac{2 + 3}{2}) g$ 118. $An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s^{- 1} and the second part of mass 2 kg moves with 8 m s^{- 1} speed. If the third part flies off with 4 m s^{- 1} speed, then its mass is$ (1) $7 kg$ (2) $17 kg$ (3) $3 kg$ (4) $5 kg$ 119. $Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius R . Coefficient of static friction between the sand layers is μ . Maximum volume of the sand can be piled up in the form of cone without slipping on the ground is$ (1) $\frac{μ R ^{3}}{3 π}$ (2) $\frac{μ R ^{3}}{3}$ (3) $\frac{π R ^{3}}{3 μ}$ (4) $\frac{μπ R ^{3}}{3}$ 120. $The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2 . The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be N (g = 10 ms^{- 2})$