Question

A stone is projected vertically up to reach maximum height h. The ratio of its potential energy to kinetic energy at height $4h/5$, will be

• A. $5:4$
• B. $4:5$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is C $1:4$

At height $h$, the kinetic energy is zero and the potential energy is $mgh$.

$P_h=mgh$ $K_h=0$

And at $h^{\prime }=\frac{4h}{5}$

potential energy will be

$P_{h^{\prime }}=mg{h}^{\prime }=\frac{4mgh}{5}$

Kinetic energy,

$K_{h^{\prime }}=mgh-\frac{4mgh}{5}=\frac{mgh}{5}$

ratio, $\frac{K_{h^{\prime }}}{P_{h^{\prime }}}=\frac{mgh/5}{4mgh/5}=\frac{1}{4}$

$K_{h^{\prime }}:P_{h^{\prime }}=1:4$

The correct option is C.