Question

Which one of the following pairs has same dimensions?

• A. Specific heat and latent heat
• B. Impulse and momentum
• C. Surface tension and force
• D. Moment of inertia and torque

Answer 1

The correct option is B Impulse and momentum

(a) Dimensions of specific heat $\left[c\right]=\left[\frac{Q}{m\Delta T}\right]$

Dimensions of latent heat $\left[L\right]=\left[\frac{Q}{m}\right]$

Not the same dimensions.

(b) Force $F=\frac{\Delta P}{\Delta t}$
Impulse $I=\Delta P=F\Delta t$

$\Rightarrow \left[I\right]=\left[P\right]$

(c) Surface tension is force per unit length
$\therefore \left[F\right]\ne \left[\frac{F}{l}\right]$

(d) Moment of inertia $I=M{R}^2$
Torque $\tau =r\times F$
Time dimension is not present in $\left[I\right]$, hence they cannot be equal.