Question

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

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

Answer 1

Answer: (B)

1 : 3

Answer 2

At the maximum height, Total energy = Potential energy =

mgh

At the height $\frac { 3 h } { 4 }$ , Potential energy = $m g \frac { 3 h } { 4 } = \frac { 3 } { 4 } m g h$

and Kinetic energy = Total energy – Potential energy $= m g h - 3 \frac { m g h } { 4 } = \frac { 1 } { 4 } m g h$

∴ $\frac { \text { Kinetic energy } } { \text { Potential energy } } = \frac { 1 } { 3 }$ .