Question

A particle is released from a height $h$ , At a certain height; its kinetic enegy is two times its potential energy. Height and speed of the particle at that instant are

• A. $\frac{h}{3},\sqrt{\frac{2 g h}{3}}$
• B. $\frac{h}{3},2\sqrt{\frac{g h}{3}}$
• C. $\frac{2 h}{3}\sqrt{\frac{2 g h}{3}}$
• D. $\frac{h}{3},\sqrt{2 g h}$

Answer 1

Answer: (B)

Total mechanical energy= $mgh$
As, $\frac{K E}{P E}=\frac{2}{1}$
$KE=\frac{2}{3}mgh$
and $PE=\frac{1}{3}mgh$
Height from the ground at this instant,
$h^{,}=\frac{h}{3} \, $
and speed of the particle at this instant,
$v=\sqrt{2 g \left(h - h^{′}\right)}$
$=\sqrt{2 g \left(\frac{2 h}{3} \, \right)}$
$=2\sqrt{\frac{g h}{3}}$