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(C) The work done by an external agent against a conservative force is equal to the change in potential energy,$W = U_f - U_i$.The gravitational poten

Vedclass · Accepted Answer

$6.67 	imes 10^{-8} \ J \ kg^{-1}$

Vedclass · Answer

(C) The work done by an external agent against a conservative force is equal to the change in potential energy,$W = U_f - U_i$.The gravitational potential $V$ at a distance $r$ from a sphere of mass $M$ is given by $V = -\frac{GM}{r}$.The initial potential at the surface $(r = 1 \ m)$ is $V_i = -\frac{G 	imes 1000}{1} = -6.67 	imes 10^{-11} 	imes 1000 = -6.67 	imes 10^{-8} \ J \ kg^{-1}$.To take the particle to infinity,the final potential is $V_f = -\frac{GM}{\infty} = 0$.The work done per unit mass is $W = V_f - V_i = 0 - (-6.67 	imes 10^{-8} \ J \ kg^{-1}) = 6.67 	imes 10^{-8} \ J \ kg^{-1}$.

$A$ particle is kept on the surface of a uniform sphere of mass $1000 \ kg$ and radius $1 \ m$. The work done per unit mass against the gravitational force between them is $\left[G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}\right]$

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