Physics · Atomic Physics

JEE Main 2025 — 4 April, Morning Shift — Question 52

A small mirror of mass mm is suspended by a massless thread of length II. Then the small angle

through which the thread will be deflected when a short pulse of laser of energy EE falls normal

on the mirror ( c=c= speed of light in vacuum and g=g= acceleration due to gravity)

  1. Option A:

    θ=2Emcgl\theta=\frac{2 E}{m c \sqrt{g l}}

    Correct
  2. Option B:

    θ=E2mcgl\theta=\frac{E}{2 m c \sqrt{g l}}

  3. Option C:

    θ=3E4mcgl\theta=\frac{3 E}{4 m c \sqrt{g l}}

  4. Option D:

    θ=Emcgl\theta=\frac{E}{m c \sqrt{g l}}

Answer: A

Step-by-step solution

Momentum of photon =hλ=EC=\frac{h}{\lambda}=\frac{E}{C} P−EC=ECP-\frac{E}{C}=\frac{E}{C}

KEi=PEfP=2Ec\mathrm{KE}_{i}=\mathrm{PE}_{f} \quad P=\frac{2 E}{c}

(2Ec)22m=mgl(1−cos⁡θ)\frac{\left(\frac{2 E}{c}\right)^{2}}{2 m}=m g l(1-\cos \theta)

4E22cm=mglθ22\frac{4 E^{2}}{2 c m}=m g l \frac{\theta^{2}}{2}

θ=2Emcgl\theta=\frac{2 E}{m c \sqrt{g l}}

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Subject
Physics
Chapter
Atomic Physics
Topic
Photon Theory of Light and Radiation Pressure
A small mirror of mass m is suspended by a massless thread of length… | JEE Main 2025 PYQ with Solution · DhiX AI