Question

A total of $4900$ joule was expended in lifting a $50\mathrm{kg}$ mass. The mass was raised to a height of

• A. $98\mathrm{m}$
• B. $960\mathrm{m}$
• C. $245\mathrm{m}$
• D. $10\mathrm{m}$

Answer 1

The correct option is D

$10\mathrm{m}$

Step 1: Given data

Mass, $m=50\mathrm{kg}$

Energy expended, $E=4900\mathrm{J}$

Step 2: Calculating the height of the mass

A body when raised to a height above ground has potential energy due to its relative position.

The potential energy of a body is given by

$P.E.=mgh$

where, $m$ is the mass of the body, $g$ is the acceleration due to gravity, and $h$ is the height above ground.

Taking $g=9.8\mathrm{m}/{\mathrm{s}}^2$ and substituting the given values, the height to which the mass was raised is given as:

$$\begin{gathered} 4900J=50kg\times 9.8m{s}^{-2}\times hm \\ \frac{4900}{50\times 9.8}=h \\ h=10m \end{gathered}$$

Thus, the mass was raised to a height of $10\mathrm{m}$.

Hence, option D is correct.