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)

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)]

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)

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)]

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 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)]

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)

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)

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 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 plane \(x+y=10\). Find the work done by this force.

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 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)]

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)

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 plane \(x+y=10\). Find the work done by this force.

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 plane \(x+y=10\). Find the work done by this force.

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.

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)

An object moving along horizontal x-direction with kinetic energy \(10\mathrm{J}\) is displaced through \(x=\left(3\hat{i}\right)\mathrm{m}\) by the force \(\vec{\mathrm{F}}=(-2\hat{i}+3\hat{j})\mathrm{N}\). The kinetic energy of the object at the end of the displacement x is :

[Re-NEET 2024]

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 body of mass ' \(m\) ' dropped from a height ' \(h\) ' reaches the ground with a speed of \(0.8 \sqrt{g h}\). The value of work done by the air-friction is: