Question

A body is projected vertically up from a point on the ground. When it is at a height $h$ above the ground, its kinetic and potential energies are found to be in the ratio of $3:2$. If the body rises to a maximum height of $H$ above the ground, then the ratio of $H:h$ will be

• A. $5:3$
• B. $2:1$
• C. $5:2$
• D. $2:5$

Answer 1

The correct option is C $5:2$

Let total M.E $=3x+2x=5x$

This M.E. will be converted into Potential energy at the maximum height.

So, Ratio of height $=$ Ratio of Potential energy

$\Rightarrow mgH:mgh=(P.E{)}_H:(P.E{)}_h$

$\Rightarrow H:h=5x:2x$ $=5:2$