Friction PYQs Set 2 (PDF)

Set 2 of 7 · Questions 31-60 of 182

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Mere Teacher · Previous Year Questions JEE Main Physics · Friction · Set 2 (Q31-60)
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31. $A given object takes n times the time to slide down 45^{\circ} rough inclined plane as it takes the time to slide down an identical perfectly smooth 45^{\circ} inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is:$ (1) $1 - \frac{1}{n ^{2}}$ (2) $1 - \frac{1}{n ^{2}}$ (3) $1 - n^{2}$ (4) $1 - n^{2}$ 32. $A 2 kg brick begins to slide over a surface which is inclined at an angle of 45^{\circ} with respect to horizontal axis. The co-efficient of static friction between their surfaces is:$ (1) $1$ (2) $1.7$ (3) $0.5$ (4) $\frac{1}{3}$ 33. $A conveyor belt is moving at a constant speed of 2m/s. A box is gently dropped on it. The coefficient of friction between them is µ= 0.5. The distance that the box will move relative to belt before coming to rest on it taking g = 10 m s^{- 2}, is:$ (1) $1.2 m$ (2) $0.6 m$ (3) $zero$ (4) $0.4 m$ 34. $A block is sliding down on an inclined plane of slope θ and at an instant t = 0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity u . The distance (S) travelled by the block before its velocity become zero, is____. (g = gravitational acceleration)$ (1) $\frac{2 u ^{2}}{cosθ}$ (2) $\frac{u ^{2}}{2 gsinθ}$ (3) $\frac{u ^{2}}{2 gcosθ}$ (4) $\frac{u ^{2}}{2 gcosθ}$ 35. $A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is:$ (1) $1470 N$ (2) $147 N$ (3) $1.47 N$ (4) $14.7 N$ 36. $A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10s. Coefficient of kinetic friction is (given, g = 10 m s^{- 2}):$ (1) $0.60$ (2) $0.75$ (3) $0.50$ (4) $0.25$ 37. $An aeroplane executes a horizontal loop at a speed of 720 kmph with its wings banked at 45^{\circ} . What is the radius of the loop? Take g = 10 m s^{- 2} .$ (1) $7.2 km$ (2) $4 km$ (3) $2 km$ (4) $4.5 km$ 38. $A bullet of mass m enters a wooden block of length L at a speed v_{1} and emerges out of block with a speed v_{2} . If F is the average force which impeded its motion through the wooden block, then (Assume uniform deceleration inside the block)$ (1) $F = \frac{m}{2 L} (v_{2}^{2} - v_{1}^{2})$ (2) $F = \frac{m}{4 L} (v_{2}^{2} + v_{1}^{2})$ (3) $F = 2 \frac{m}{L} (v_{2} - v_{1})^{2}$ (4) $F = \frac{m}{2 L} (v_{2} + v_{1})^{2}$ 39. $A block of mass m is placed on a surface having vertical cross section given by y = x^{2} /4 . If coefficient of friction is 0.5 , the maximum height above the ground at which block can be placed without slipping is:$ (1) $1/4 m$ (2) $1/2 m$ (3) $1/6 m$ (4) $1/3 m$ 40. $A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is: [Take g = 10 m/ s^{- 2}]$ (1) $2 m$ (2) $0.5 m$ (3) $3.2m$ (4) $0.8ms$ 41. $A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30^{\circ} . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: (g = 10 m / s^{2}, 3 = 1.73)$ (1) $264 m / s$ (2) $51.4 m / s$ (3) $70.4 m / s$ (4) $102.8 m / s$ 42. $A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30º the box starts to slip and slides 4.0 m down the plank in 4.0s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:$ (1) $0.6 and 0.5$ (2) $0.5 and 0.6$ (3) $0.4 and 0.3$ (4) $0.6 and 0.6$ 43. $A car is negotiating a curved road of radius R . The road is banked at angle θ . The coefficient of friction between the tyres of the car and the road is μ_{s} . The maximum safe velocity on this road is [NEET 2016]$ (1) $gR (\frac{μ _{s} + tan θ}{1 - μ _{s} tan θ})$ (2) $\frac{g}{R} (\frac{μ _{s} + tan θ}{1 - μ _{s} tan θ})$ (3) $\frac{g}{R ^{2}} (\frac{μ _{s} + tan θ}{1 - μ _{s} tan θ})$ (4) $g R^{2} (\frac{μ _{s} + tan θ}{1 - μ _{s} tan θ})$ 44. $Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:$ (1) $g, \frac{g}{3}$ (2) $\frac{g}{3}, g$ (3) $g, g$ (4) $\frac{g}{3}, \frac{g}{3}$ 45. $A ball of mass 2 g released from the top of an inclined plane describes a circular motion of radius 20 cm in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is$ (1) $20 cm$ (2) $10 cm$ (3) $50 cm$ (4) $60 cm$ 46. $Two masses M1 and .M2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M2 is twice that of M1 the acceleration of the system is a_{1} . When the mass M2 is thrice that of M1. The acceleration of The system is a_{2} . The ratio \frac{a _{1}}{a _{2}} will$ (1) $\frac{1}{3}$ (2) $\frac{2}{3}$ (3) $\frac{3}{2}$ (4) $\frac{1}{2}$ 47. $A body of weight 50 N is placed on a horizontal surface as shown in the figure. The minimum force required to move the body is 28.28 N . The frictional force and the normal reaction are respectively.$ (1) $10 N, 15 N$ (2) $20 N, 30 N$ (3) $2 N, 3 N$ (4) $5 N, 6 N$ 48. $A block of mass 10 kg placed on rough horizontal surface having coefficient of friction μ = 0.5, if a horizontal force of 100 N acting on it then acceleration of the block will be$ (1) $10 m / s^{2}$ (2) $5 m / s^{2}$ (3) $15 m / s^{2}$ (4) $0.5 m / s^{2}$ 49. $A car of mass ' m' moves on a banked road having radius ' r' and banking angle θ . To avoid slipping from banked road, the maximum permissible speed of the car is v_{0} . The coefficient of friction μ between the wheels of the car and the banked road is$ (1) $μ = \frac{v _{o}^{2} + rg tan θ}{rg + v _{o}^{2} tan θ}$ (2) $μ = \frac{v _{0}^{2} - rg tan θ}{rg - v _{0}^{2} tan θ}$ (3) $μ = \frac{v _{0}^{2} - rg tan θ}{rg + v _{0}^{2} tan θ}$ (4) $μ = \frac{v _{o}^{2} + rg tan θ}{rg - v _{o}^{2} tan θ}$ 50. $A block rests on a rough inclined plane making an angle of 30^{\circ} with the horizontal. The coefticient of static friction between the block and the plane is 0.8 . If the frictional force on the block is 10 N, the mass of the block is (g = 10 m s^{- 2}))$ (1) $1 kg$ (2) $2 kg$ (3) $3 kg$ (4) $4 kg$ 51. $A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force F applied perpendicular to the incline. If the mass of the box is 1 kg, the angle of inclination is 30^{\circ} and the coefficient of static friction between the box and the inclined plane is 0.2 , the minimum magnitude of F is (Use g = 10 m / s^{2})$ (1) $0 N, as 30^{\circ} is less than angle of repose$ (2) $\geq1 N$ (3) $\geq3.3 N$ (4) $\geq16.3 N$ 52. $In the system shown in the figure, the acceleration of 1 kg block is$ (1) $\frac{g}{2} downwards$ (2) $\frac{g}{2} upwards$ (3) $\frac{g}{4} downwards$ (4) $\frac{g}{4} upwards$ 53. $The system of two masses 2 kg and 3 kg as shown in the figure is released from rest. The work done on 3 kg block by the force of gravity during first 2 seconds of its motion is (g = 10 ms^{- 2})$ (1) $120 J$ (2) $80 J$ (3) $40 J$ (4) $30 J$ 54. $When a body is placed on a rough plane (coefficient of friction = μ) inclined at an angle θ to the horizontal, its acceleration is\dots\dots\dots (acceleration due to gravity = g)$ (1) $g (sin θ - μ cos θ)$ (2) $g (sin θ - cos θ)$ (3) $gμ (sin θ - cos θ)$ (4) $g (μ sin θ - cos θ)$ 55. $A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown infigure. The coefficient of kinetic friction is μ_{K} Then, the block's acceleration ’ a ’ is given by: (g is accelerationdue to gravity)$ (1) $- \frac{F}{m} cos θ - μ_{K} (g - \frac{F}{m} sin θ)$ (2) $\frac{F}{m} cos θ - μ_{K} (g - \frac{F}{m} sin θ)$ (3) $\frac{F}{m} cos θ - μ_{K} (g + \frac{F}{m} sin θ)$ (4) $\frac{F}{m} cos θ + μ_{K} (g - \frac{F}{m} sin θ)$ 56. $A uniform chain of length 'L' has one of its ends attached to the wall at point 'A', while \frac{3 L}{4} of the length of chain is lying on table as shown in figure. The minimum coefficient of friction between table and chain so that chain remains in equilibrium -$ (1) $\frac{1}{3}$ (2) $\frac{1}{4}$ (3) $\frac{3}{4}$ (4) $\frac{1}{5}$ 57. $The upper half of an inclined plane of inclination Θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by$ (1) $μ = 2 t an Θ$ (2) $μ = t an Θ$ (3) $μ = \frac{1}{t an Θ}$ (4) $μ = \frac{2}{t an Θ}$ 58. $A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m . The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m / s^{2})$ (1) $10 n r a d / s$ (2) $10 rad/s$ (3) $\frac{10}{2 π} r a d / s$ (4) $10 r a d / s$ 59. $In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force F required to slide the block C with constant speed is____N. (Use g = 10 m / s^{2})$ 60. $A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is\dots\dots..m.$