Question

A stone is projected vertically upward to reach maximum height h. The ratio of its kinetic energy to its potential energy at a height $\frac{4}{5} h, $ will be

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

Answer 1

Answer: (C)

At a height $\frac{4}{5} h, $
$\text{Potential energy} = \text{mg} \times \frac{4 h }{5} = \frac{4}{5} \text{mgh}$
Total energy = mgh
$\therefore \text{K E at that height} = \text{mgh} - \frac{4}{5} mgh = \frac{1}{5} mgh ⁡$
$\therefore \text{At a height} \frac{4}{5} h , ⁡ \text{the ratio of}$
$\frac{\text{KE}}{\text{PE}} = \frac{\frac{1}{5} \text{mgh}}{\frac{4}{5} \text{mgh}} = \frac{1}{4}$