Question

Two bodies of mass $40\mathrm{kg}$ and $45\mathrm{kg}$ are placed on the $10\mathrm{th}$ floor of a building. Which of the body possesses greater potential energy?

Answer 1

Step 1:

Given data:

The mass of the first body = $40\mathrm{kg}$

Mass of the second body = $45\mathrm{kg}$

Both are placed at $10\mathrm{th}$ floor of the same building.

Step 2:

Formula used:

$$\begin{gathered} \mathrm{We}\mathrm{know}, \\ \mathrm{PE}=\mathrm{mgh} \\ \mathrm{We}\mathrm{can}\mathrm{say}\mathrm{that}, \\ \mathrm{The}\mathrm{potential}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{body}\left(\mathrm{PE}\right)\propto \mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{body}\left(\mathrm{m}\right),\mathrm{and} \\ \mathrm{Potential}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{body}\left(\mathrm{PE}\right)\propto \mathrm{height}\mathrm{of}\mathrm{the}\mathrm{body}\mathrm{from}\mathrm{the}\mathrm{ground}\left(\mathrm{h}\right) \end{gathered}$$

Step 3:

Comparison of the potential energy of both the bodies:

$$\begin{gathered} \mathrm{As}\mathrm{both}\mathrm{are}\mathrm{kept}\mathrm{at}\mathrm{equal}\mathrm{height}\mathrm{from}\mathrm{the}\mathrm{ground}, \\ \mathrm{Thus}, \\ \mathrm{Between}\mathrm{the}\mathrm{two}\mathrm{bodies}\mathrm{of}\mathrm{mass}40\mathrm{kg}\mathrm{and}45\mathrm{kg}, \\ \mathrm{The}\mathrm{body}\mathrm{having}\mathrm{mass}45\mathrm{kg}\mathrm{will}\mathrm{have}\mathrm{more}\mathrm{potential}\mathrm{energy}. \end{gathered}$$