Dimensional Analysis

Easyphysics

If Force (F), Velocity (V), and Time (T) are taken as fundamental units, then the dimensions of Mass are:

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$[F V T^{-} 1]$

$[F V T^{-} 2]$

$[F V^{-} 1 T]$

$[F V^{-} 1 T^{-} 1]$

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Subject: physics
Chapter: units and dimensions
Topic: dimensional analysis
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

$[F V^{-} 1 T]$

Basic Relation: $F = m \times a$ , where $a$ is acceleration.
Acceleration in terms of V and T: $a = \frac{Δ v}{Δ t} ⟹ [a] = [V] [T]^{- 1}$ .
Rearrange for Mass: $M = \frac{F}{a} ⟹ [M] = [F] / [V] [T]^{- 1}$ .
Final Expression: $[M] = [F V^{- 1} T^{1}]$ .

This easy difficulty physics question is from the chapter units and dimensions, covering the topic of dimensional analysis. It appeared in the 2025 exam.

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