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Physics · Units, Dimensions & Error Analysis

JEE Main 2024 — 5 April, Shift 1 — Question 32

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimension as that the uG\sqrt{\mathrm{uG}} :

  1. Option A:

    Pressure gradient per unit mass

  2. Option B:

    Force per unit mass

    Correct
  3. Option C:

    Gravitational potential

  4. Option D:

    Energy per unit mass

Answer: B

Step-by-step solution

[uuG]=[(M1 L−1 T−2)(M−1 L3 T−2)][u \mathrm{uG}]=\left[\left(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right)\left(\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right)\right]

[uG]=[M0 L2 T−4][\mathrm{uG}]=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-4}\right]

[uG]=[L1 T−2][\sqrt{\mathrm{uG}}]=\left[\mathrm{L}^{1} \mathrm{~T}^{-2}\right]

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
5 April, Shift 1
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis

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