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

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) (h/3),√(2 g h/3) (B) (h/3),2√(g h/3) (C) (2 h/3)√(2 g h/3) (D) (h/3),√2 g h

Tardigrade Admin · Accepted Answer

Total mechanical energy= mgh As, (K E/P E)=(2/1) KE=(2/3)mgh and PE=(1/3)mgh Height from the ground at this instant, h,=(h/3) and speed of the particle at this instant, v=√2 g (h - hâ²) =√2 g ((2 h/3) ) =2√(g h/3)

Q. 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

$\frac{h}{3}, \frac{2 g h}{3}$

$\frac{h}{3}, 2 \frac{g h}{3}$

$\frac{2 h}{3} \frac{2 g h}{3}$

$\frac{h}{3}, 2 g h$

Total mechanical energy= $m g h$
As, $\frac{K E}{PE} = \frac{2}{1}$
$K E = \frac{2}{3} m g h$
and $PE = \frac{1}{3} m g h$
Height from the ground at this instant,
$h^{,} = \frac{h}{3}$
and speed of the particle at this instant,
$v = 2 g (h - h^{'})$
$= 2 g (\frac{2 h}{3})$
$= 2 \frac{g h}{3}$

Q. 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

3h​,32gh​​

3h​,23gh​​

32h​32gh​​

3h​,2gh​