Newton's Laws of Motion PYQs Set 2 (PDF)

Set 2 of 7 · Questions 31-60 of 197

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Mere Teacher · Previous Year Questions JEE Main Physics · Newton's Laws of Motion · Set 2 (Q31-60)
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31. $Consider the following statements A and B. Identify the correct choice in the given answers. (A) In an inelastic collision, there is no loss in kinetic energy during collision. (B) During a collision, the linear momentum of the entire system of particles is conserved if there is no external force acting on the system.$ (1) $Both A and B are wrong.$ (2) $Both A and B are correct.$ (3) $A is wrong and B is correct.$ (4) $A is correct and B is wrong.$ 32. $A ball of mass 0.2 kg moving with a speed of 20 m / s is brought to rest in 0.1 s . The average force applied to the ball is$ (1) $20 N$ (2) $30 N$ (3) $40 N$ (4) $60 N$ 33. $One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is (T is the tension in the string)$ (1) $T + \frac{m v ^{2}}{l}$ (2) $0$ (3) $T$ (4) $T - \frac{m v ^{2}}{l}$ 34. $A motor car moving with velocity 7 m / s stops in 10 m distance when brakes are applied. What is the relation between the resistance force (R) and the weight (W) of the car? (Take value of g = 9.8 m / s^{2})$ (1) $R = W$ (2) $R = - W$ (3) $R = - \frac{W}{2}$ (4) $R = - \frac{W}{4}$ 35. $A body of mass 0.6 kg is moving along a circular path of radius 1 m . If the body moves with \frac{900}{π} revolutions per minute, its kinetic energy$ (1) $120 J$ (2) $270 J$ (3) $360 J$ (4) $240 J$ 36. $A spring of force constant 15 N / m is cut into two pieces. If the ratio of their length is 1 : 3, then the force constant of smaller piece is____N/m.$ (1) $60$ (2) $15$ (3) $20$ (4) $45$ 37. $If mass, speed and radius of the circular path of the particle are increased by 100 %, then the necessary force required to maintain the circular path will have to be increased by$ (1) $100 %$ (2) $250 %$ (3) $300 %$ (4) $400 %$ 38. $A bullet of mass 20 g has an initial speed of 1 ms^{- 1} just before it starts penetrating a mud wall of thickness 20cm. If the wall offers a mean resistance of 2.5 \times 10^{- 2} N, the speed of the bullet after emerging from the other side of the wall is close to:$ (1) $0.1 ms^{- 1}$ (2) $0.7 ms^{- 1}$ (3) $0.3 ms^{- 1}$ (4) $0.4 ms^{- 1}$ 39. $A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm . If the blocktakes 40 s to complete one round, the normal force by the side walls of the groove is:$ (1) $0.0314 N$ (2) $9.859 \times 10^{- 2} N$ (3) $6.28 \times 10^{- 3} N$ (4) $9.859 \times 10^{- 4} N$ 40. $A point object moves along an arc of a circle of radius R . Its velocity depends upon the distance covered s as v = K s where K is a constant. If θ is the angle between the total acceleration and tangential acceleration, then$ (1) $tan θ = \frac{s}{R}$ (2) $tan θ = \frac{s}{2 R}$ (3) $tan θ = \frac{s}{2 R}$ (4) $tan θ = \frac{2 s}{R}$ 41. $A particle of mass m falls from rest through a resistive medium having resistive force, F = - kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t)?$ (1) (2) (3) (4) 42. $An aircraft is moving with uniform velocity 150 m / s in the space. If all the forces acting on it are balanced, then it will$ (1) $keep moving with same velocity$ (2) $remain floating at its place$ (3) $escape in space$ (4) $fall down on earth.$ 43. $A body of mass 4 kg experiences two forces F_{1} = 5 i + 8 j + 7 k and F_{2} = 3 i - 4 j - 3 k . Find the acceleration 6 the body$ (1) $3 m / s^{2}$ (2) $2 m / s^{2}$ (3) $6 m / s^{2}$ (4) $5 m / s^{2}$ 44. $A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 m s^{- 1}, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is$ (1) $117.6 kg s^{- 1}$ (2) $58.6 kg s^{- 1}$ (3) $6 kg s^{- 1}$ (4) $76.4 kg s^{- 1}$ 45. $A body of mass 50 kg is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, the reading of the spring balance is$ (1) $= 0$ (2) $< 50 kg$ (3) $= 50 kg$ (4) $> 50 kg$ 46. $A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is 30^{\circ} . Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is____。$ (1) $\frac{3}{2} mg$ (2) $mg$ (3) $\frac{1}{2} mg$ (4) $3 mg$ 47. $Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are$ (1) $12 N, 6 N$ (2) $13 N, 5N$ (3) $10 N, 8 N$ (4) $16 N, 2 N$ 48. $For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is$ (1) $a child revolving in a giant wheel$ (2) $a driver in a sports car moving with a constant high speed of 200 km h^{- 1} on a straight rod$ (3) $the pilot of an aeroplane which is taking off$ (4) $a cyclist negotiating a sharp curve.$ 49. $A particle of mass ' m' moves along a circle of radius ' r' with constant tangential acceleration. If K.E. of the particle is ' E' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is$ (1) $\frac{E}{2 πrm}$ (2) $\frac{E}{6 πrm}$ (3) $\frac{E}{8 πrm}$ (4) $\frac{E}{4 πrm}$ 50. $A body of mass 0.05 kg is observed to fall with an acceleration of 9.5 m s^{- 2} . The opposing force of air on the body is (g = 9.8 m s^{- 2}) .$ (1) $0.015 N$ (2) $0.15 N$ (3) $0.030 N$ (4) $zero$ 51. $A particle of mass m is moving in a straight line with line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3 p . Here k is a constant. The value of T is:$ (1) $2 \frac{k}{p}$ (2) $2 \frac{p}{k}$ (3) $\frac{2 k}{p}$ (4) $\frac{2 p}{k}$ 52. $A force (F) = - 5 i - 7 j + 3 k acting on a particle causes a displacement (s) = 3 i - 2 j + ak in its own direction. If the work done is 14 J, then the value of a is$ (1) $0$ (2) $5$ (3) $15$ (4) $1$ 53. $The angular speed of a particle moving in a circular path is doubled. Then, the centripetal acceleration of the particle is$ (1) $4 times the initial centripetal acceleration$ (2) $halved$ (3) $doubled$ (4) $unchanged$ 54. $A 10 N force is applied on a body produce in it an acceleration of 1 m/ s^{2} . The mass of the body is$ (1) $15 kg$ (2) $20 kg$ (3) $10 kg$ (4) $5 kg$ 55. $A massless spring gets elongated by amount x_{1} under a tension of 5 N. Its elongation is x_{2} under the tension of 7 N. For the elongation of (5 x_{1} - 2 x_{2}), the tension in the spring will be,$ (1) $39 N$ (2) $15 N$ (3) $11 N$ (4) $20 N$ 56. $A car of mass 1500 kg is moving with 20 ms^{- 1} . velocity. If the breaks are applied it comes to rest in 5 seconds, then the retarding force is$ (1) $9000 N$ (2) $6000 N$ (3) $12000 N$ (4) $3000 N$ 57. $A body of mass 6 kg is moving with a uniform velocity 4 ms^{- 1} . Its velocity changes to 6 ms^{- 1} when a force of 12 N acts on it. Then its displacement is$ (1) $3 m$ (2) $5 m$ (3) $8 m$ (4) $12 m$ 58. $A body of mass 2 kg moving with velocity of v_{in} = 3 i + 4 j ms^{- 1} enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \frac{5}{3} seconds, then velocity of the body when it emerges from force field is.$ (1) $3 i + 4 j + 5 k$ (2) $4 i + 3 j + 5 k$ (3) $3 i + 4 j - 5 k$ (4) $3 i + 4 j + 5 k$ 59. $A ball is thrown upward with an initial velocity V_{0} from the surface of the earth. The motion of the ball is affected by a drag force equal to mγ v^{2} (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:$ (1) $\frac{1}{γ g} tan^{- 1} (\frac{γ}{g} V_{0})$ (2) $\frac{1}{γ g} sin^{- 1} (\frac{γ}{g} V_{0})$ (3) $\frac{1}{γ g} ln (1 + \frac{γ}{g} V_{0})$ (4) $\frac{1}{2 γ g} tan^{- 1} (\frac{2 γ}{g} V_{0})$ 60. $A body of mass 2 kg moves under a force of (2 i + 3 j + 5 k) N . It starts from rest and was at the origininitially. After 4 s its new coordinates are (8, b, 20) . The value of b is. (Round off to the Nearest Integer)$