Work, Energy & Power PYQs Set 1 (PDF)

Set 1 of 10 · Questions 1-30 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Work, Energy & Power · Set 1 (Q1-30)
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1. $An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg . The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m / s . The frictional force opposing the motion is 6000 N . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m / s^{2}) must be at least:$ (1) $66000 W$ (2) $63248 W$ (3) $48000 W$ (4) $56320 W$ 2. $A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.$ (1) $\frac{S}{4}, \frac{3 gS}{2}$ (2) $\frac{S}{2}, \frac{3 gS}{2}$ (3) $\frac{S}{4}, \frac{3 gS}{2}$ (4) $\frac{S}{2}, \frac{3 gS}{2}$ 3. $A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest$ (1) $at the highest position of the body.$ (2) $at the instant just before the body hits the earth.$ (3) $it remains constant all through.$ (4) $at the instant just after the body is projected.$ 4. $A particle experiences a variable force F = (4 x i + 3 y^{2} j) in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, the Kinetic Energy changes by$ (1) $50.0 J$ (2) $12.5 J$ (3) $25.0J$ (4) $0J$ 5. $The energy required to break one bond in DNA is 10^{- 20} J. This value (in eV) is nearly [NEET 2020]$ (1) $0.6$ (2) $0.06$ (3) $0.006$ (4) $6$ 6. $A particle moves from a point (- 2 i + 5 j) to (4 j + 3 k) when a force of (4 i + 3 j) N is applied. How much work has been done by the force? [NEET 2016]$ (1) $8 J$ (2) $11 J$ (3) $5 J$ (4) $2 J$ 7. $Two similar springs P and Q have spring constants K_{P} and K_{Q}, such that K_{P} > K_{Q} . They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs W_{P} and W_{Q} are related as, in case (a) and case (b), respectively$ (1) $W_{P} = W_{Q}; W_{P} = W_{Q}$ (2) $W_{P} > W_{Q}; W_{Q} > W_{P}$ (3) $W_{P} < W_{Q}; W_{Q} < W_{P}$ (4) $W_{P} = W_{Q}; W_{P} > W_{Q}$ 8. $A mass of 1 kg is thrown up with a velocity of 100 \frac{m}{s} . After 5 seconds, it explodes into two parts. One-part of mass 400 g comes down with a velocity 25 \frac{m}{s} . The velocity of other part is (Take g = 10 m s^{- 2})$ (1) $40 m / s$ (2) $80 m / s$ (3) $100 m / s$ (4) $60 m / s$ 9. $A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg . The velocity of 18 kg mass is 6 m s^{- 1} . The kinetic energy of the other mass is$ (1) $324 J$ (2) $486 J$ (3) $256 J$ (4) $524 J.$ 10. $A smooth chain of length 2 m is kept on a table such that its length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg . The work done in pulling the entire chain on the table is (taking g = 10 m / s^{2})$ (1) $3.6 J$ (2) $12.9 J$ (3) $2.0 J$ (4) $6.3 J$ 11. $A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4 , then the work done against friction (in J) is :$ (1) $4200$ (2) $3900$ (3) $4000$ (4) $4500$ 12. $An elastic spring of unstretched length L and force constant k is stretched by a small length x . It is further stretched by another small length y . Work done during the second stretching is$ (1) $\frac{ky}{2} (x + 2 y)$ (2) $\frac{k}{2} (2 x + y)$ (3) $ky (x + 2 y)$ (4) $\frac{ky}{2} (2 x + y)$ 13. $A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest, the force on the particle at time t is?$ (1) $\frac{mk}{2} t^{- 1/2}$ (2) $mk t^{- 1/2}$ (3) $2 mk t^{- 1/2}$ (4) $\frac{1}{2} mk t^{- 1/2}$ 14. $A force of 4 N acts on a 10 kg body initially at rest. Let W_{1} is work done by force during 0 \leq t \leq 1 s . Likewise W_{2} is the work done by force during 1 s \leq t \leq 2 s, where t is time in second. The ratio \frac{W _{2}}{W _{1}}, is$ (1) $1$ (2) $2$ (3) $\frac{1}{2}$ (4) $3$ 15. $If the potential energy between two molecules is given by U = - \frac{A}{r ^{6}} + \frac{B}{r ^{12}}, then at equilibrium, separation between molecules, and the potential energy are$ (1) $(\frac{2 B}{A})^{\frac{1}{6}}, - \frac{A ^{2}}{2 B}$ (2) $(\frac{B}{2 A})^{\frac{1}{6}}, - \frac{A ^{2}}{2 B}$ (3) $(\frac{2 B}{A})^{\frac{1}{6}}, - \frac{A ^{2}}{4 B}$ (4) $(\frac{B}{A})^{\frac{1}{6}}, 0$ 16. $A stationary particle breaks into two parts of masses m_{A} and m_{B} which move with velocities v_{A} and v_{B} respectively. The ratio of their kinetic energies (K_{B} : K_{A}) is:$ (1) $v_{B} : v_{A}$ (2) $m_{B} : m_{A}$ (3) $m_{B} v_{B} : m_{A} v_{A}$ (4) $1 : 1$ 17. $A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg . If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to: (1 HP = 746 W, g = 10 m s^{- 2})$ (1) $1.9 m / s$ (2) $1.7 m / s$ (3) $2 m / s$ (4) $1.5 m / s$ 18. $An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:$ (1) $(\frac{9 P}{8 m})^{\frac{1}{2}} t^{\frac{3}{2}}$ (2) $(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{2}{3}}$ (3) $(\frac{9 m}{8 P})^{\frac{1}{2}} t^{\frac{3}{2}}$ (4) $(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{3}{2}}$ 19. $Two masses of 1 g and 9 g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is$ (1) $1 : 9$ (2) $9 : 1$ (3) $1 : 3$ (4) $3 : 1$ 20. $A force acts on a body of mass 10 kg, resulting in its displacement given as x = (\frac{t ^{3}}{25}) m, where t is the time in seconds. The work done by the force in 5 s is$ (1) $620 J$ (2) $333 J$ (3) $524 J$ (4) $None$ 21. $A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 \times 1 0^{7} J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 m s^{-2}$ (1) $6.45 \times 1 0^{-3} kg$ (2) $9.89 \times 1 0^{-3} kg$ (3) $12.89 \times 1 0^{-3} kg$ (4) $2.45 \times 1 0^{-3} kg$ 22. $A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s^{- 1} . It collides with a horizontal spring of force constant 200 N m^{- 1} . The maximum compression produced in the spring will be$ (1) $0.5 m$ (2) $0.6 m$ (3) $0.7 m$ (4) $0.2 m$ 23. $A body of mass 1 kg begins to move under the action of a time dependent force F = (2 t i + 3 t^{2} j) N, where i and j are unit vectors along X and Y axes. What power will be developed by the force at the time (t) ? [NEET 2016]$ (1) $(2 t^{2} + 4 t^{4}) W$ (2) $(2 t^{3} + 3 t^{4}) W$ (3) $(2 t^{3} + 3 t^{5}) W$ (4) $(2 t + 3 t^{3}) W$ 24. $A block of mass 10 kg, moving in x -direction with a constant speed of 10 ms^{- 1}, is subjected to a retarding force F = 0.1 \times J / m during its travel from x = 20 m to 30 m. Its final KE will be$ (1) $475 J$ (2) $450 J$ (3) $275 J$ (4) $250 J$ 25. $If F = (60 i + 15 j - 3 k) N and v = (2 i - 4 j + 5 k) m / s, then instantaneous power is$ (1) $195 watt$ (2) $45 watt$ (3) $75 watt$ (4) $100 watt.$ 26. $A particle which is experiencing a force, given by F = 3 i^- 12 j^, undergoes a displacement of d = 4 i^. If the particle had a kinetic energy of 3J at the beginning of the displacement, what is kinetic energy at the end of the displacement?$ (1) $9 J$ (2) $15 J$ (3) $10 J$ (4) $12 J$ 27. $Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s^{- 1} . Take ‘g’ constant with a value 10 m s^{- 2} . The work done by the (i) gravitational force and the (ii) resistive force of air is$ (1) $(i) 1.25 J (ii) - 8.25 J$ (2) $(i) 100 J (ii) 8.75 J$ (3) $(i) 10 J (ii) - 8.75 J$ (4) $(i) - 10 J (ii) -8.25J$ 28. $A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3 . The smaller fragment moves with a velocity of 6 m s^{- 1} . The kinetic energy of the larger fragment is$ (1) $96 J$ (2) $216 J$ (3) $144 J$ (4) $360 J$ 29. $A ball having kinetic energy KE, is projected at an angle of 60^{\circ} from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?$ (1) $\frac{( KE )}{8}$ (2) $\frac{( KE )}{2}$ (3) $\frac{( KE )}{16}$ (4) $\frac{( KE )}{4}$ 30. $A force (3 x^{2} + 2 x - 5) N displaces a body from x = 2 m to x = 4 m . Work done by this force is ______J$