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 change in gravitational potential energy if a particle of mass $2kg$ is taken from the origin to the point $(12m,5m)$

• A. $-225J$
• B. $-240J$
• C. $-245J$
• D. $-250J$

Answer 1

Answer: (B)

$-240J$

$dV=-\overrightarrow{E}\overrightarrow{dr}=-(5\hat{i}+12\hat{j})(12\hat{i}+5\hat{j})$

$=-(60+60)=-120$

Therefore, change in gravitational potential energy

$U=mdV=2\times (-120)=-240J$