Question

A mass m falls from rest under the influence of gravity. Then the average power supplied to the mass by the force of gravity is

• A. $P=m\sqrt{\frac{g^{3}h}{3}}$
• B. $P=m\sqrt{\frac{g^{3}h}{12}}$
• C. $P=2m\sqrt{\frac{g^{3}h}{2}}$
• D. $P=m\sqrt{\frac{g^{3}h}{2}}$
  where h is the distance the mass falls.

Answer 1

The correct option is D $P=m\sqrt{\frac{g^{3}h}{2}}$

where h is the distance the mass falls.
$W=Pt=mgh\dots \dots \left(1\right)h=\frac{1}{2}g{t}^{2}t=\sqrt{\frac{2h}{g}}\dots \dots \left(2\right)\left(2\right)in\left(1\right)P\sqrt{\frac{2h}{g}}=mghP=m\sqrt{\frac{g^{3}h}{2}}$