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Physics · Units, Dimensions & Error Analysis

JEE Main 2025 — 29 January, Morning Shift — Question 28

The expression given below shows the variation of velocity (v) with time ( tt ),

v=At2+BtC+tv=A t^{2}+\frac{B t}{C+t}. The dimension of ABC is :

  1. Option A:

    [M0 L2 T−3]\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-3}\right]

    Correct
  2. Option B:

    [M0 LlT−3]\left[\mathrm{M}^{0} \mathrm{~L}^{\mathrm{l}} \mathrm{T}^{-3}\right]

  3. Option C:

    [M0 LlT−2]\left[\mathrm{M}^{0} \mathrm{~L}^{\mathrm{l}} \mathrm{T}^{-2}\right]

  4. Option D:

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

Answer: A

Step-by-step solution

[LT−1]=[A][T2]=[B][T][C]+[T]\left[\mathrm{LT}^{-1}\right]=[\mathrm{A}]\left[\mathrm{T}^{2}\right]=\frac{[\mathrm{B}][\mathrm{T}]}{[\mathrm{C}]+[\mathrm{T}]} [C]=[T][\mathrm{C}]=[\mathrm{T}]

[A]=[LT−3][\mathrm{A}]=\left[\mathrm{LT}^{-3}\right]

[B]=[LT−1][\mathrm{B}]=\left[\mathrm{LT}^{-1}\right]

[ABC]=[L2 T−3][\mathrm{ABC}]=\left[\mathrm{L}^{2} \mathrm{~T}^{-3}\right]

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Paper
29 January, Morning Shift
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis

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