Question

A stone projected vertically upwards from the ground reaches a maximum height h. When it is at a height $\frac{3h}{4}$, the ratio of its kinetic and potential energies is

• A. 3 : 4
• B. 1 : 3
• C. 4 : 3
• D. 3 : 1

Answer 1

The correct option is B

1 : 3

According to conservation of energy,$KineticEnergy+PotentialEnergy=constant$
At the maximum height, Total energy = Potential energy = mgh

At the height $\frac{3h}{4}$ , Potential energy = $=mg\frac{3h}{4}=\frac{3}{4}mgh$ and Kinetic energy = Total energy – Potential energy $=mgh-3\frac{mgh}{4}=\frac{1}{4}mgh$

$\therefore \frac{Kineticenergy}{Potentialenergy}=\frac{1}{3}$