JEE Advanced 2018 · Paper 2 · Physics Q1

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PhysicsMultiple correct+4 / -2Question 1 of 54

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$ -axis. Its kinetic energy $K$ changes with time as $dK/dt = \gamma t$ , where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

The force applied on the particle is constant

The speed of the particle is proportional to time

The distance of the particle from the origin increases linearly with time

The force is conservative

Answer and worked solution

Official answer: A, B, D

Kinetic energy. $K=\dfrac{\gamma t^2}2$ , since $K=0$ at $t=0$ .

Speed. $\tfrac12mv^2=\tfrac12\gamma t^2\implies v=\sqrt{\dfrac\gamma m}\,t$ , so $v\propto t$ . (B) is true.

Force. $a=\dfrac{dv}{dt}=\sqrt{\gamma/m}$ is constant, so $F=ma$ is constant. (A) is true.

Distance. $x=\tfrac12at^2\propto t^2$ , not linear in $t$ . (C) is false.

Conservative? A constant force is conservative: its work depends only on the end points, with $U=-Fx$ . (D) is true.

(A), (B), (D)

Topics:Work-energy theorem Power Motion in a straight line

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JEE Advanced 2018 · Paper 2, Physics question 1