The gravitational field in a region is given by equation $\mathbf{E}=(5 \mathbf{i}+12 \mathbf{j}) \mathrm{N}…
The gravitational field in a region is given by equation $\mathbf{E}=(5 \mathbf{i}+12 \mathbf{j}) \mathrm{N} / \mathrm{kg}$. If a particle of mass $2 \mathrm{~kg}$ is moved from the origin to the point $(12 \mathrm{~m}, 5 \mathrm{~m})$ in this region, the change in gravitational potential energy is
$-225 \mathrm{~J}$
$-240 \mathrm{~J}$
$-245 \mathrm{~J}$
$-250 \mathrm{~J}$
Solution
We have,
$\begin{aligned} d V & =-E \cdot d r=-(5 \mathbf{i}+12 \mathbf{j}) \cdot(12 \mathbf{i}+15 \mathbf{j}) \\ & =(60+60)=-120\end{aligned}$
The change in gravitational potential energy
$U=m d V=2 \times(-120)=-240 \mathrm{~J}$