JEE Main 2025 January Physics: Work, Energy, Power & Collisions – Previous Year Questions

A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

A force $\vec F=2\hat i+b\hat j+\hat k$ 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.

A force $\vec f=x^2y\,\hat i+y^2\hat j$ acts on a particle in a plane $x+y=10$. The work done by this force during a displacement from (0, 0) to (4m, 2m) is Joule (round off to the nearest integer)

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 $\alpha=1$ N then $\beta$ will be

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

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 $\vec F=(2\hat i+3\hat j)$N, it moves to a new point Q having coordinates (6, 10)m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of :

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

As shown below, bob A of a pendulum having massless string of length ‘R’ is released from $60^\circ$ to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take $g$ as acceleration due to gravity.)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_A=5$ m/s, $v_B=2$ m/s, $v_C=4$ m/s. If we wait sufficiently long for elastic collision to happen, then $v_A=4$ m/s, $v_B=2$ m/s, $v_C=5$ m/s will be the final velocities.
Reason (R) : In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below :