Work, Energy & Power PYQs Set 2 (PDF)

Set 2 of 10 · Questions 31-60 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Work, Energy & Power · Set 2 (Q31-60)
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31. $A metal chain of mass 2 kg and length 90 cm over hangs a table with 60 cm on the table. How much work needs to be done to put the hanging part of the chain back on the table? (Let g = 10 m / s^{2})$ (1) $2 J$ (2) $10 J$ (3) $1 J$ (4) $3 J$ 32. $A 1 kg box placed at the origin starts sliding along x -axis under the action of a force F = Fi . Its acceleration as a function of x is given by a (x) = β . x where β = 5 s^{- 2} . The work done by F in moving the box from x = 2 cm to x = 5 cm in joule is$ (1) $52.5 \times 10^{- 4}$ (2) $105.5 \times 10^{- 4}$ (3) $17.0 \times 10^{- 4}$ (4) $34.0 \times 10^{- 4}$ 33. $Two particles of masses m_{1}, m_{2} move with initial velocities u_{1} and u_{2} . On collision, one of the particles get excited to higher level, after absorbing energy s . Iffinal velocities ofparticles be v_{1} and v_{2} then we must have$ (1) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} - ϵ = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$ (2) $\frac{1}{2} m_{1}^{2} u_{1}^{2} + \frac{1}{2} m_{2}^{2} u_{2}^{2} + ϵ = \frac{1}{2} m_{1}^{2} v_{1}^{2} + \frac{1}{2} m_{2}^{2} v_{2}^{2}$ (3) $m_{1}^{2} u_{1} + m_{2}^{2} u_{2} - ϵ = m_{1}^{2} v_{1} + m_{2}^{2} v_{2}$ (4) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} - ϵ$ 34. $A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of$ (1) $2 : 1$ (2) $1 : 4$ (3) $1: 2$ (4) $1: 2$ 35. $A particle of mass m moves in a circular orbit under the central potential field, U (r) = \frac{- C}{r}, where C is apositive constant. The correct radius - velocity graph of the particle's motion is:$ (1) (2) (3) (4) 36. $A sand dropper drops sand of mass m (t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e. \frac{dm}{dt} \propto v . If P is the power delivered to run the belt at constant speed then which of the following relationship is true?$ (1) $P \propto v$ (2) $P \propto v$ (3) $P^{2} \propto v^{5}$ (4) $P^{2} \propto v^{3}$ 37. $A force F = α + β x^{2} acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant α = 1 N then β will be$ (1) $15 N / m^{2}$ (2) $12 N / m^{2}$ (3) $8 N / m^{2}$ (4) $10 N / m^{2}$ 38. $A body of mass 10 kg is acted upon by a force given by equation F = (3 t^{2} - 30) newtons. The initial velocity of the body is 10 m / s . The velocity of the body after 5 s is$ (1) $4.5 m / s$ (2) $6 m / s$ (3) $7.5 m / s$ (4) $5 m / s$ 39. $A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k^{2} r t^{2} . where k is a constant. The power delivered to the particle by the force acting on it is given as$ (1) $zero$ (2) $m k^{2} r^{2} t^{2}$ (3) $m k^{2} r^{2} t$ (4) $m k^{2} rt$ 40. $The potential energy of a long spring when stretched by 2 cm is U . If the spring is stretched by 8 cm, potential energy stored in it will be [NEET 2023]$ (1) $4 U$ (2) $8 U$ (3) $16 U$ (4) $2 U$ 41. $A stone of mass in, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is:$ (1) $the same throughout the motion$ (2) $minimum at the highest position of the circular path$ (3) $minimum at the lowest position of the circular path$ (4) $minimum when the rope is in the horizontal position$ 42. $A particle of mass M is moving in a horizontal circle ofradius R with uniform speed v . Whenit moves from one point to a diametrically opposite point, its$ (1) $kinetic energy change by M v^{2} /4$ (2) $momentum does not change$ (3) $momentum change by 2 Mv$ (4) $kinetic energy changes by M v^{2}$ 43. $A particle with total energy E is moving in a potential energy region U_{(x)} . Motion of the particle is restricted to the region when (NEET2013)$ (1) $U (x) < E$ (2) $U (x) = 0$ (3) $U(x)\leqE$ (4) $U (x) > E$ 44. $If momentum of a body is increased by 20%, then its kinetic energy increases by:$ (1) $36%$ (2) $40%$ (3) $44%$ (4) $48%$ 45. $A force acts on a 3 g particle in such a way that the position of the particle as a function of time is given by x = 3 t - 4 t^{2} + t^{3}, where x is in metres and t is in seconds. The work done during the first 4 second is$ (1) $490 mJ$ (2) $450 mJ$ (3) $576 mJ$ (4) $530 mJ.$ 46. $A uniform force of (3 i + j) newton acts on a particle of mass 2 kg . Hence the particle is displaced from position (2 i + k) metre to position (4 i + 3 j - k) metre. The work done by the force on the particle is (NEET2013)$ (1) $13J$ (2) $15J$ (3) $9J$ (4) $6J$ 47. $The potential energy function (in J) of a particle in a region of space is given as U = (2 x^{2} + 3 y^{3} + 2 z) . Here x, y and z are in meter. The magnitude of x - component of force (in N) acting on the particle at point P (1, 2, 3) m is :$ (1) $2$ (2) $6$ (3) $4$ (4) $8$ 48. $A bullet of mass m moving horizontally with speed v_{0} hits a wooden block of mass M that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height h, then how much of the initial kinetic energy of the bullet is lost in the collision?$ (1) $\frac{1}{2} m v_{0}^{2} (\frac{M}{m + M})$ (2) $\frac{1}{2} m v_{0}^{2} (\frac{M + m}{M})$ (3) $\frac{1}{2} m v_{0}^{2} (\frac{M ^{2}}{( m + M ) ^{2}})$ (4) $\frac{1}{2} m v_{0}^{2} (\frac{( M + m ) ^{2}}{M ^{2}})$ 49. $Two particles of masses m_{1} and m_{2} have equal kinetic energies. The ratio of their momenta is$ (1) $m_{1} : m_{2}$ (2) $m_{2} : m_{1}$ (3) $m_{1} : m_{2}$ (4) $m_{1}^{2} : m_{2}^{2}$ 50. $An object of mass 1000 g experiences a time dependent force F = (2 t i + 3 t^{2} j) N . The power generated by the force at time t is:$ (1) $(2 t^{2} + 18 t^{3}) W$ (2) $(3 t^{3} + 5 t^{5}) w$ (3) $(2 t^{3} + 3 t^{5}) w$ (4) $(2 t^{2} + 3 t^{3}) w$ 51. $A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8 \times 10^{- 4} J by the end of the second revolution after the beginning of the motion? [NEET 2016]$ (1) $0.15 m / s^{2}$ (2) $0.18 m / s^{2}$ (3) $0.2 m / s^{2}$ (4) $0.1 m / s^{2}$ 52. $A horizontal force F = (g - x^{2}) i N acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from x = 0 to x = 3 m (in J) is (Use g = 10 m / s^{2})$ (1) $24$ (2) $35$ (3) $30$ (4) $21$ 53. $A body of mass 3 kg is moving under the action of a force which causes a displacement of (\frac{t ^{3}}{3}) m, where ' t' is time in seconds. The work done by the force in first 2 seconds is$ (1) $2 J$ (2) $3.8 J$ (3) $5.2 J$ (4) $24 J$ 54. $A body is initially at rest. It undergoes one dimensional motion with constant acceleration. "The power delivered to it at time t is proportional to$ (1) $t^{3/2}$ (2) $t^{2}$ (3) $t^{1/2}$ (4) $t$ 55. $A force acts on a body of mass 15 kg, initially at rest. If the instantaneous power due to the force at the end of the third second is 5 W, then the instantaneous power (in W) at the end of the 4 s will be$ (1) $6.33$ (2) $6.67$ (3) $6.29$ (4) $6.94$ 56. $Two bodies with kinetic energies in the ratio of 4 : 1 are moving with equal linear momentum. The ratio of their masses is$ (1) $4: 1$ (2) $1 : 1$ (3) $1 : 2$ (4) $1 : 4.$ 57. $The kinetic energy acquired by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to$ (1) $m$ (2) $m^{0}$ (3) $m$ (4) $1/ m .$ 58. $A motor engine pumps 1800 L of water per minute from a well of depth 30 m and allows to pass through a pipe of cross-sectional area 30 cm^{2} . Then the power of the engine is (Acceleration due to gravity, g = 10 ms^{- 2})$ (1) $20.5 kW$ (2) $15.5 kW$ (3) $10.5 kW$ (4) $9.5 kW$ 59. $A body of mass 4 kg is placed on a plane at a point P having coordinate (3, 4) m . Under the action of force F = (2 i + 3 j) N, it moves to a new point Q having coordinates (6, 10) m in 4 sec. The average power and instanteous power at the end of 4 sec are in the ratio of:$ (1) $13 : 6$ (2) $4 : 3$ (3) $1 : 2$ (4) $6 : 13$ 60. $A body of mass 2 kg is driven by an engine delivering a constant power of 1 J / s . The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m)$