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Physics · Work, Power & Energy

JEE Advanced 2018 — Paper 2 — Question 1

A particle of mass mm 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=γt\mathrm{dK} / \mathrm{dt}=\gamma \mathrm{t}, where γ\gamma is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

  1. Option A:

    The force applied on the particle is constant

    Correct
  2. Option B:

    The speed of the particle is proportional to time

    Correct
  3. Option C:

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

  4. Option D:

    The force is conservative

    Correct

Answer: A, B, D

Step-by-step solution

dKdt=γt, So K=γt2212mv2=γt22 or v=tγ mdvdt=γm F=mγ\begin{aligned} & \frac{\mathrm{dK}}{\mathrm{dt}}=\gamma \mathrm{t}, \text { So } \quad \mathrm{K}=\frac{\gamma \mathrm{t}^{2}}{2} \\& \frac{1}{2} \mathrm{mv}^{2}=\frac{\gamma \mathrm{t}^{2}}{2} \text { or } \mathrm{v}=\mathrm{t} \sqrt{\frac{\gamma}{\mathrm{~m}}} \\& \frac{\mathrm{dv}}{\mathrm{dt}}=\sqrt{\frac{\gamma}{\mathrm{m}}} \\& \mathrm{~F}=\sqrt{\mathrm{m} \gamma} \end{aligned}

(i) force is constant.

(ii) speed is proportional to tt

(iii) Force is constant, so it is conservative

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2018
Paper
Paper 2
Subject
Physics
Chapter
Work, Power & Energy
Topic
Kinetic Energy and Work-Energy Theorem

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