Question

The gravitational field in a region is given by $\overrightarrow{E}=\left(5N{kg}^{-1}\right)\overrightarrow{i}+\left(12N{kg}^{-1}\right)\overrightarrow{j}$. Find the potential at the points $(12m,0)$ and $(0,5m)$ if the potential at the origin is taken to be zero.

• A. $-30J{kg}^{-1},-30J{kg}^{-1}$
• B. $-40J{kg}^{-1},-30J{kg}^{-1}$
• C. $-60K{kg}^{-1},-60J{kg}^{-1}$
• D. $-40J{kg}^{-1},-50J{kg}^{-1}$

Answer 1

The correct option is C $-60K{kg}^{-1},-60J{kg}^{-1}$

$V=-{\int }_{x_1}^{x_2}E.dx$

$⟹V_{(12,0)}-V_{(0,0)}=-\left(5\right)\left(12\right)=-60Jk{g}^{-1}$

And similarly $V_{(0,5)}-V_{(0,0)}=-\left(12\right)\left(5\right)=-60Jk{g}^{-1}$