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(B) The gravitational field is given by $E = (5\hat{i} + 12\hat{j}) \,N/kg$. The displacement vector $dr$ from the origin $(0, 0)$ to the point $(12 \

Vedclass · Accepted Answer

$-240$

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(B) The gravitational field is given by $E = (5\hat{i} + 12\hat{j}) \,N/kg$. The displacement vector $dr$ from the origin $(0, 0)$ to the point $(12 \,m, 5 \,m)$ is $dr = (12\hat{i} + 5\hat{j}) \,m$. The change in gravitational potential $dV$ is given by $dV = -E \cdot dr$. $dV = -(5\hat{i} + 12\hat{j}) \cdot (12\hat{i} + 5\hat{j}) = -(5 	imes 12 + 12 	imes 5) = -(60 + 60) = -120 \,J/kg$. The change in gravitational potential energy $\Delta U$ is given by $\Delta U = m \cdot dV$. Given mass $m = 2 \,kg$, we have $\Delta U = 2 \,kg 	imes (-120 \,J/kg) = -240 \,J$.

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?

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