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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
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The correct answer is:
$-240 \mathrm{~J}$
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
$U=m d V=2 \times(-120)=-240 \mathrm{~J}$
$\begin{aligned} d V & =-E \cdot d r=-(5 \mathbf{i}+12 \mathbf{j}) \cdot(12 \mathbf{i}+15 \mathbf{j}) \\ & =(60+60)=-120\end{aligned}$
The change in gravitational potential energy
$U=m d V=2 \times(-120)=-240 \mathrm{~J}$
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