\[(a)\;\frac{-GMm}{R} \quad (b)\;\frac{GMm}{R} \quad (c)\;\frac{GMm}{2R} \quad (d)\;can\;not\;be\;calculated\]

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Work done=increase in potential energy of system

$\qquad=V_f-V_i$

$\qquad=m(V_f-V_i)\qquad V-$ gravitational potential

Even if mass is not distributed uniformly potential at center is $\large\frac{-GM}{R}$

$W= m \bigg[ 0-\bigg(\large\frac{-GM}{R}\bigg)\bigg]$

$\qquad= \large\frac{GMm}{R}$

Hence b is the correct answer.

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