When a body is projected vertically up, its PE is twice its KE, when it is at a height h above the ground. At what height will its KE be twice the KE ?

Question

When a body is projected vertically up, its PE is twice its KE, when it is at a height h above the ground. At what height will its KE be twice the KE ? (A) 2h (B) (h/3) (C) (h/2) (D) (h/4)

Tardigrade Admin · Accepted Answer

Total energy, E1=PE+KE =PE+(1/2)PE=(3/2)PE=(3/2)mgh E2=PE+KE=PE+2PE+3PE=3mgh As, E2=E1⇒ 3mgh'=(3/2)mgh⇒ h'=(h/2)

Q. When a body is projected vertically up, its PE is twice its KE, when it is at a height $h$ above the ground. At what height will its KE be twice the KE ?

$2 h$

$\frac{h}{3}$

$\frac{h}{2}$

$\frac{h}{4}$

Total energy, $E_{1} = PE + K E$
$= PE + \frac{1}{2} PE = \frac{3}{2} PE = \frac{3}{2} m g h$
$E_{2} = PE + K E = PE + 2 PE + 3 PE = 3 m g h$
As, $E_{2} = E_{1} \Rightarrow 3 m g h^{'} = \frac{3}{2} m g h \Rightarrow h^{'} = \frac{h}{2}$

Q. When a body is projected vertically up, its PE is twice its KE, when it is at a height h above the ground. At what height will its KE be twice the KE ?

2h

3h​

2h​

4h​