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(D) The work done to move a particle from the surface of a sphere to infinity is equal to the change in gravitational potential energy,which is the ne

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$6.67 	imes 10^{-10} \, J$

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(D) The work done to move a particle from the surface of a sphere to infinity is equal to the change in gravitational potential energy,which is the negative of the potential energy at the surface.$W = U_{\infty} - U_{surface} = 0 - (- \frac{GMm}{R}) = \frac{GMm}{R}$Given:$M = 100 \, kg$$m = 10 \, g = 0.01 \, kg$$R = 10 \, cm = 0.1 \, m$$G = 6.67 	imes 10^{-11} \, Nm^2/kg^2$Substituting the values:$W = \frac{6.67 	imes 10^{-11} 	imes 100 	imes 0.01}{0.1}$$W = \frac{6.67 	imes 10^{-11} 	imes 1}{0.1}$$W = 6.67 	imes 10^{-10} \, J$

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and a radius of $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (Take $G = 6.67 \times 10^{-11} \, Nm^2/kg^2$)

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