Question

A mango is falling from the branch of a tree at a height h from the ground. After it has fallen a height of $\frac{h}{2}$, it will possess:

• A. only potential energy.
• B. only kinetic energy.
• C. half kinetic and half potential energy.
• D. more kinetic and less potential energy.

Answer 1

The correct option is C

half kinetic and half potential energy.

Initial speed, u =0

Initial kinetic energy =0

Let Initial height above the ground be H

Then final height above the ground be $\frac{H}{2}$

Let Final speed at height $\frac{H}{2}bev.$

Now, $v^2=u^2+2as$

$\Rightarrow v^2=2\times g\times \frac{H}{2}$

$\Rightarrow v=\sqrt{gH}$

$\therefore$ Final $K.E=\frac{1}{2}m{v}^2=\frac{1}{2}mgH$

and, Final potential energy at height $\frac{H}{2}=\frac{mgH}{2}$

and total energy $=K.E+P.E=\frac{mgH}{2}+\frac{mgH}{2}=mgH$

Hence, at height $\frac{H}{2}$, mango will have half potential and half kinetic energy.