The gravitational field in a region is given | vedclass

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(B) Given,gravitational field $E = (5 \hat{i} + 12 \hat{j}) 	ext{ N kg}^{-1}$,mass $m = 2 	ext{ kg}$,and displacement vector $r = (12 \hat{i} + 15 \

Vedclass · Accepted Answer

$-480$

Vedclass · Answer

(B) Given,gravitational field $E = (5 \hat{i} + 12 \hat{j}) 	ext{ N kg}^{-1}$,mass $m = 2 	ext{ kg}$,and displacement vector $r = (12 \hat{i} + 15 \hat{j}) 	ext{ m}$.The work done by the gravitational field is $W = \int F \cdot dr = \int (mE) \cdot dr$.The change in gravitational potential energy $\Delta U$ is given by $\Delta U = -W = -m \int E \cdot dr$.Substituting the values:$\Delta U = -2 \int_{(0,0)}^{(12,15)} (5 \hat{i} + 12 \hat{j}) \cdot (dx \hat{i} + dy \hat{j})$$\Delta U = -2 \left[ \int_0^{12} 5 dx + \int_0^{15} 12 dy ight]$$\Delta U = -2 [5(12 - 0) + 12(15 - 0)]$$\Delta U = -2 [60 + 180]$$\Delta U = -2 [240] = -480 	ext{ J}$.Thus,the change in gravitational potential energy is $-480 	ext{ J}$.Therefore,the correct option is $B$.

The gravitational field in a region is given by $E = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. If a particle of mass $2 \text{ kg}$ is moved from the origin to the point $(12 \text{ m}, 15 \text{ m})$ in this region,the change in gravitational potential energy is (in $\text{ J}$)

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