Work, Energy and Power

Read the following statements carefully and choose the correct option.

Assertion: Work done by a central force is independent of the path.

Reason: Potential energy is associated with every force.

(Shift - I Memory Based)

Two bodies A and B of equal mass are suspended from two massless springs of spring constant \({k}_{1}\) and \({k}_{2}\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

[JEE Main 2025, 29 Jan (Shift 2)]

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?

[JEE Main 2025, 23 Jan (Shift 2)]

The displacement of a particle moving under the action of a force \(\vec{\mathrm{F}}=2\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+\hat{\mathrm{k}}\) is \(\vec{\mathrm{d}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\). Find the value of \(b\) if the work done by the force is zero.

(Shift II Memory Based)

A small mirror of mass m is suspended by a massless thread of length \(l\). Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror
(c = speed of light in vacuum and g = acceleration due to gravity)

[JEE Main 2025, 4 Apr (Shift 1)]

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?

[JEE Main 2025, 23 Jan (Shift 2)]

A force \(\overset{⃗}{F}={x}^{2}y\hat{i}+{y}^{2}\hat{j}\)​ acts on a body. The body is moved from the point \((0,0)\) to \((4,2)\) along the line \(x+y=10\). Find the work done by this force.

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\)

Assertion A: In a central force field, the work done is independent of the path chosen.
Reason R: Every force encountered in mechanics does not have an associated potential energy.

In the light of the above statements, choose the most appropriate answer from the options given below

[JEE Main 2025, 28 Jan (Shift 1)]

Read the following statements carefully and choose the correct option.

Assertion: Work done by a central force is independent of the path.

Reason: Potential energy is associated with every force.

(Shift - I Memory Based)

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\)

Assertion A: In a central force field, the work done is independent of the path chosen.
Reason R: Every force encountered in mechanics does not have an associated potential energy.

In the light of the above statements, choose the most appropriate answer from the options given below

[JEE Main 2025, 28 Jan (Shift 1)]

A force \(\vec{\mathrm{F}}=2\hat{i}+\mathrm{b}\hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2\hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

[JEE Main 2025, 22 Jan (Shift 2)]

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be

[JEE Main 2024, 06 Apr (Shift 2)]

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be

[JEE Main 2024, 06 Apr (Shift 2)]

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to

A force \(\overset{⃗}{F}={x}^{2}y\hat{i}+{y}^{2}\hat{j}\)​ acts on a body. The body is moved from the point \((0,0)\) to \((4,2)\) along the line \(x+y=10\). Find the work done by this force.

A projectile is projected at an angle of 60 degree with the horizontal with kinetic energy K. Find the kinetic energy of the projectile at the highest point.

(Shift - II Memory Based)

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 \(g=10m/s²\))

[02 April, 2026 (Shift-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.

[JEE Main 2025, 3 Apr (Shift 1)]

An object of mass \(1000\mathrm{g}\) experiences a time dependent force \(\vec{\mathrm{F}}=\left(2\mathrm{t}\hat{\mathrm{i}}+3{\mathrm{t}}^{2}\hat{\mathrm{j}}\right)\mathrm{N}\). The power generated by the force at time t is :

[JEE Main 2025, 7 Apr (Shift 1)]

A body of mass ' m ' connected to a massless and unstretchable string goes in vertical circle of radius ' R ' under gravity g . The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n\sqrt{gR}\), where, \(n⩾1\), then ratio of kinetic energy of the body at bottom to that at top of the circle is

[JEE Main 2025, 29 Jan (Shift 1)]

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. \(\frac{dm}{dt}\propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

[JEE Main 2025, 29 Jan (Shift 2)]

A force \(\vec{\mathrm{F}}=2\hat{i}+\mathrm{b}\hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2\hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

Two bodies A and B of equal mass are suspended from two massless springs of spring constant \({k}_{1}\) and \({k}_{2}\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

[JEE Main 2025, 29 Jan (Shift 2)]

A force \(F=\alpha +\beta {x}^{2}\) 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 \(\alpha =1N\) then \(\beta\) will be

[JEE Main 2025, 24 Jan (Shift 1)]

Given below are two statements:

Statement I: An object moves from position r₁ to position r₂ under a conservative force field \(\vec{F.}\) The work done by the force is \(W=−{\int }_{{r}_{1}}^{{r}_{2}}\vec{F}⋅\vec{dr}\)

Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 22 Jan (Shift 2)]

A ball of mass \(100\text{ }\text{g}\) is thrown with a speed of \(20\text{ }\text{m/s}\) at an angle of \(6{0}^{∘}\) with the horizontal. Calculate the decrease in the kinetic energy of the ball from the point of projection to the point where it reaches its maximum height.

(Shift II Memory Based)

The displacement of a particle moving under the action of a force \(\vec{\mathrm{F}}=2\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+\hat{\mathrm{k}}\) is \(\vec{\mathrm{d}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\). Find the value of \(b\) if the work done by the force is zero.

(Shift II Memory Based)

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy ( k) on reaching the surface of earth. The values of v and k respectively are __________
(Take radius of earth to be 6400 km and \(g=9.8m/{s}^{2}\) )

[02 April, 2026 (Shift-2)]

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 \(xm(\mathrm{x}<2)\) from the wall. the speed of the block will be :

[JEE Main 2025, 8 Apr (Shift 1)]

A projectile is projected at an angle of 60 degree with the horizontal with kinetic energy K. Find the kinetic energy of the projectile at the highest point.

(Shift - II Memory Based)

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 \(5m/s\).The work done by the unknown resistive force is _____ J.
(take \(g=10m/{s}^{2}\) )

A bullet of mass \(50\mathrm{g}\) is fired with a speed \(100\mathrm{m}/\mathrm{s}\) on a plywood and emerges with \(40\mathrm{m}/\mathrm{s}\). The percentage loss of kinetic energy is:

[JEE Main 2024, 06 Apr (Shift 1)]

A bullet of mass \(50\mathrm{g}\) is fired with a speed \(100\mathrm{m}/\mathrm{s}\) on a plywood and emerges with \(40\mathrm{m}/\mathrm{s}\). The percentage loss of kinetic energy is:

[JEE Main 2024, 06 Apr (Shift 1)]

A body of mass ' m ' connected to a massless and unstretchable string goes in vertical circle of radius ' R ' under gravity g . The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n\sqrt{gR}\), where, \(n⩾1\), then ratio of kinetic energy of the body at bottom to that at top of the circle is

[JEE Main 2025, 29 Jan (Shift 1)]

Two bodies A and B of equal mass are suspended from two massless springs of spring constant \({k}_{1}\) and \({k}_{2}\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

A ball of mass \(100\text{ }\text{g}\) is thrown with a speed of \(20\text{ }\text{m/s}\) at an angle of \(6{0}^{∘}\) with the horizontal. Calculate the decrease in the kinetic energy of the ball from the point of projection to the point where it reaches its maximum height.

(Shift II Memory Based)

Two bodies A and B of equal mass are suspended from two massless springs of spring constant \({k}_{1}\) and \({k}_{2}\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

[JEE Main 2025, 29 Jan (Shift 2)]

A force \(\mathrm{F}=\alpha +{\mathrm{βx}}^{2}\) 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 \(\alpha =1\mathrm{N}\) then \(\beta\) will be

[JEE Main 2025, 24 Jan (Shift 1)]

A body of mass 1 kg moves along a straight line with a velocity \(v=2{x}^{2}\) . The work done by the body during displacement from x = 0 to 5 m is _______J.

[JEE Main 2026, 6 Apr (Shift 2)]

Given below are two statements:

Statement I: An object moves from position r₁ to position r₂ under a conservative force field \(\vec{F.}\) The work done by the force is \(W=−{\int }_{{r}_{1}}^{{r}_{2}}\vec{F}⋅\vec{dr}\)

Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 22 Jan (Shift 2)]

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to

[JEE Main 2024, 05 Apr (Shift 2)]

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to

[JEE Main 2024, 05 Apr (Shift 2)]

Which one of the following forces cannot be expressed in terms of potential energy?

[JEE Main 2025, 7 Apr (Shift 2)]

Identify the correct statements from the following:
A. Work done by a person in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
C. Work done by friction on a body sliding down an inclined plane is positive.
D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
E. Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

[JEE Main 2023, 29 Jan (Shift 2)]

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

[JEE Main 2020, 6 Sep (Shift 1)]

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be

[JEE Main 2021, 20 Jul (Shift 2)]

Water falls from a \(40 \mathrm{~m}\) high dam at the rate of \(9 \times 10^{4} \mathrm{~kg}\) per hour. Fifty percent of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of \(100 \mathrm{~W}\) lamps, that can be lit, is: (Take \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

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 :

[JEE Main 2021, 18 March (Shift 1)]

If the kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be

The ratio of powers of two motors is \(\frac{3 \sqrt{x}}{\sqrt{x}+1}\), that are capable of raising \(300 \mathrm{~kg}\) water in 5 minutes and \(50 \mathrm{~kg}\) water in 2 minutes respectively from a well of \(100 \mathrm{~m}\) deep. The value of \(x\) will be

[JEE Main 2023, 13 Apr (Shift 1)]

A porter lifts a heavy suitcase of mass \(80 \mathrm{~kg}\) and at the destination lowers it down by a distance of \(80 \mathrm{~cm}\) with a constant velocity. Calculate the work done by the porter in lowering the suitcase.
(take \(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\) )

[JEE Main 2021, 22 Jul (Shift 2)]

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time ' \(t\) ' is proportional to:

[JEE Main 2017, 8 Jan (Shift 1)]