Question

A body of mass $2kg$ is thrown vertically upwards with K.E. $245J$. The acceleration due to gravity is $9.8m{s}^{-2}$. The K.E. of the body will become half at a height of

• A. $25m$
• B. $12.5m$
• C. $6.25m$
• D. $5m$

Answer 1

The correct option is C

$6.25m$

Step 1: Given data

The maximum potential energy of the body$=245J$.

Mass of the body, $m=2kg$

acceleration due to gravity is $g=9.8m{s}^{-2}$

Step 2: Calculating the height

The maximum kinetic energy is equal to the potential energy attained by the body at the topmost point.

Calculate the height of the body using the equation,

$\mathrm{Potential}\mathrm{energy}=\mathrm{m}gh$, where $\mathrm{m}$ is the mass, $g$ is the acceleration due to gravity and $h$ is the maximum height attained by the body.

Therefore,

$$\begin{gathered} 245J=2kg\times 9.8m{s}^{-2}\times h \\ h=\frac{245}{2\times 9.8} \\ h=12.5m \end{gathered}$$

The kinetic energy and potential energy are half at the middle point of the total height.

The height is calculated below:

$h=\frac{12.5}{2}m=6.25m$.

The K.E. of the body will become half at a height of $6.25m$

Hence, option (c) is correct