First slide

Dimensions of physical quantities

Question

If velocity, time and force were chosen as basic quantities, find the dimensions of mass and energy.

Moderate

A

$[mass] = [{FTv}^{- 1}], [Energy] = [FTv]$
B

$[mass] = [{FTv}^{- 2}], [Energy] = [FTv]$
C

$[mass] = [{FTv}^{- 3}], [Energy] = [FTv]$
D

$[mass] = [{FTv}^{- 4}], [Energy] = [FTv]$

Solution

We know that,
$Force = mass \times acceleration = mass \times \frac{velocity}{time} \Rightarrow mass = \frac{force x time}{velocity} O r [mass] = \frac{[force] \times [time]}{[velocity]} = \frac{[F] [T]}{[v]} [mass] = [{FTv}^{- 1}]$
Dimensions of energy are same as the dimensions of kinetic energy
$[Energy] = [\frac{1}{2} m v^{2}] = [m] [v]^{2} = [{FTv}^{- 1}] [v]^{2} = [FTv]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App