Work-Energy Theorem PYQs: JEE Mains Physics

Showing 1–37 of 37 questions

1. 1. A body of mass \(1\) kg moves along a straight line with a velocity \(v = 2x^2\). The work done by the body during displacement from \(x = 0\) to \(5\) m is __________ J. 2026 Medium
2. 2. A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\)) 2026 Medium
3. 3. The rain drop of mass \(1\) g, starts with zero velocity from a height of \(1\) km. It hits the ground with a speed of \(5\) m/s. The work done by the unknown resistive force is _______ J. (take \(g = 10\) m/s\(^2\)) 2026 Medium
4. 4. A bead of mass ' \(m\) ' slides without friction on the wall of a vertical circular hoop of radius ' \(R\) ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' \(R\) '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)
   2025 Hard
5. 5. A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is \(200 \mathrm{~N} / \mathrm{m}\). The block is pushed such that the length of the spring becomes 1 m and then released. At distance \(\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)\) from the wall. the speed of the block will be : 2025 Medium
6. 6. 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. 2025 Easy
7. 7. A body of \(\mathrm{m} \mathrm{kg}\) slides from rest along the curve of vertical circle from point \(A\) to \(B\) in friction less path. The velocity of the body at \(B\) is _______. (given, \(\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\sqrt{2}=1.4\) )
   2024 Hard
8. 8. A particle is placed at the point \(\mathrm{A}\) of a frictionless track \(A B C\) as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point \(B\) is _______. \(\left(\right.\) Take \(g=10 \mathrm{~m} / \mathrm{s}^2\) ).
   2024 Hard
9. 9. A particle of mass \(m\) moves on a straight line with its velocity increasing with distance according to the equation \(\mathrm{v}=\alpha \sqrt{\mathrm{x}}\), where \(\alpha\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(\mathrm{x}=0\) to \(\mathrm{x}=\mathrm{d}\), will be _______. 2024 Hard
10. 10. A particle of mass \(10\,g\) moves in a straight line with retarcation \(2x\), where \(x\) is the displacement in \(SI\) units. Its loss of kinetic energy for above displacement is \(\left(\frac{10}{x}\right)^{- n }\, J\). The value of \(n\) will be \(............\). 2023 Hard
11. 11. Given below are two statements: Statement \(I:\) A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. Statement \(II:\) A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below. 2023 Medium
12. 12. A block of mass ' \(m\) ' (as shown in figure) moving with kinetic energy \(E\) compresses a spring through a distance \(25\,cm\) when, its speed is halved. The value of spring constant of used spring will be \(nE\; Nm ^{-1}\) for \(n=\)
    2022 Hard
13. 13. A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\) 2022 Medium
14. 14. A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)
    2022 Hard
15. 15. A particle experiences a variable force \(\overrightarrow{ F }=\left(4 x \hat{ i }+3 y ^{2} \hat{ j }\right)\) 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............\(j\) 2022 Medium
16. 16. A particle of mass \(500 \,gm\) is moving in a straight line with velocity \(v=b x^{5 / 2}\). The work done by the net force during its displacement from \(x=0\) to \(x =4 \,m\) is ...................\(J\) (Take \(b =0.25 \,m ^{-3 / 2} s ^{-1}\) ) 2022 Medium
17. 17. In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................
    2022 Medium
18. 18. Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )
    2022 Hard
19. 19. A body of mass ' \({m}\) ' dropped from a height ' \({h}\) ' reaches the ground with a speed of \(0.8 \sqrt{{gh}}\). The value of workdone by the air-friction is \(.....\,{mgh}\) 2021 Hard
20. 20. A boy is rolling a \(0.5\, kg\) ball on the frictionless floor with the speed of \(20\, ms ^{-1}\). The ball gets deflected by an obstacle on the way. After deflection it moves with \(5 \%\) of its initial kinetic energy. What is the speed of the ball now ? (in \(ms ^{-1}\)) 2021 Medium
21. 21. A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\)) 2021 Medium
22. 22. An engine is attached to a wagon through a shock absorber of length \(1.5\, {m}\). The system with a total mass of \(40,000\, {kg}\) is moving with a speed of \(72\, {kmh}^{-1}\) when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by \(1.0\, {m}\). If \(90\, \%\) of energy of the wagon is lost due to friction, the spring constant is \(....\, \times 10^{5}\, {N} / {m}\) 2021 Hard
23. 23. As shown in the figure, a particle of mass \(10\) \(kg\) is placed at a point \(A\). When the particle is slightly displaced to its right, it starts moving and reaches the point \(B\). The speed of the particle at \(B\) is \(x\, m / s\). (Take \(\left. g =10\, m / s ^{2}\right)\) The value of \('x'\) to the nearest integer is.........
    2021 Medium
24. 24. A cricket ball of mass \(0.15\, kg\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20 \;m\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2\, m\) while launching the ball, the value of \(F(\) in \(N)\) is  \(\left(g=10\, m s^{-2}\right)\) 2020 Medium
25. 25. A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\) 2019 Medium
26. 26. A force acts on a \(2\,kg\) object so that its position is given as a function of time as \(x= 3t^2 + 5.\) What is the work done by this force in first \(5\,seconds\) ? ................ \(\mathrm{J}\) 2019 Medium
27. 27. A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled \(3\, m\) is ................ \(\mathrm{J}\)
    2019 Medium
28. 28. A particle which is experiencing a force, given by \(\vec F = 3\vec i -12\vec j\), undergoes a displacement of \(\vec d = 4\vec i\) . If the particle had a kinetic energy of \(3\, J\) at the beginning of the displacement, what is its kinetic energy at the end of the displacement? 2019 Medium
29. 29. A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be 2019 Hard
30. 30. A wedge of mass \(M = 4\,m\) lies on a frictionless plane. A particle of mass \(m\) approaches the wedge with speed \(v\). There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by 2019 Medium
31. 31. A particle is moving in a circular path of radius a under the action of an attractive potential \(U = - \frac{k}{{2{r^2}}}\) Its total energy is 2018 Medium
32. 32. A body of mass \(m= 10^{-2}\) \(kg\) is moving in a medium and experiences a frictional force \(F= -kv^2\). Its initial speed is \(v_0= 10\) \(ms^{-1}\). If, after \(10\; s\), its energy is \(\frac{1}{8}\) \(mv_0^2\) the value of \(k\) will be 2017 Hard
33. 33. A time dependent force \(F = 6t\) acts on a particle of mass \(1\ kg\). If the particle starts from rest, the work done by the force during the first \(1\) secand will be ............... \(\mathrm{J}\) 2017 Hard
34. 34. A point particle of mass, moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). The particle is released, from rest, from the point \(P\) and it comes to rest at a point \(R\). The energies, lost by the ball, over the parts, \(PQ\) and \(PR\), of the track, are equal to each other, and no energy is lost when particle changes direction from \(PQ\) to \(QR\). The values of the coefficient of friction \(\mu\) and the distance \(x(=QR)\) are, respecitvely close to
    2016 Hard
35. 35. Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)
    2016 Hard
36. 36. A block of mass \(m = 10\,kg\) rests on a horizontal table. The coefficient of friction between the block and the table is \(0.05.\) When hit by a bullet of mass \(50\,g\) moving with speed \(v,\) that gets embedded in it, the block moves and comes to stop after moving a distance of \(2\,m\) on the table. If a freely falling object were to acquire speed \(\frac {v}{10}\) after being dropped from height \(H,\) then neglecting energy losses and taking \(g = 10\,ms^{-2},\) the value of \(H\) is close to ................. \(\mathrm{km}\) 2015 Hard
37. 37. A bullet looses \({\left( {\frac{1}{n}} \right)^{th}}\) of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be 2014 Hard

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