Question

Which of the following pairs have identical dimensions?

• A. Momentum and force
• B. Pressure and surface tension
• C. Moment of force and angular momentum
• D. Surface tension and surface energy

Answer 1

The correct option is D Surface tension and surface energy

(A) : Relation between momentum and force is given by $F=\frac{dP}{dt}$
So momentum and force have different dimensions.
(B) : Pressure is force per unit area whereas surface tension is force per unit length.
So pressure and surface tension have different dimensions.
(C) : Relation between moment of force and angular momentum is given by $\tau =\frac{dL}{dt}$
So momentum of force and angular momentum have different dimensions.
(D) : Relation between surface energy $E/A$ and surface tension $T$ i given by $E=TA$
$\therefore$ $\frac{E}{A}=T$
So surface tension and surface energy have identical dimensions.