A particle is released from a height H . At certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are

Question

A particle is released from a height H . At certain height its kinetic energy is two times its potential energy. Height and speed of 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

∴ K+U=mgH K=2U ∴ 2U+U=mgH ⇒ U=(m g H/3) ⇒ mgh=(m g H/3) ⇒ h=H / 3 ∴ (1/2) m v2=2U=(2 m g H/3) ⇒ v=2√(g H/3)

Q. A particle is released from a height $H$ . At certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are

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

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

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

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

$∴ K + U = m g H$ & $K = 2 U$
$∴ 2 U + U = m g H$
$\Rightarrow U = \frac{m g H}{3} \Rightarrow m g h = \frac{m g H}{3} \Rightarrow h = H /3$
$∴ \frac{1}{2} m v^{2} = 2 U = \frac{2 m g H}{3} \Rightarrow v = 2 \frac{g H}{3}$

Q. A particle is released from a height H . At certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are

3H​,32gH​​

3H​ , 23gH​​

32H​ , 32gH​​

3H​ , 2gH​