From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R/2$ is removed, as shown in the figure. Taking gravitational potential $V=0$ at $r = \infty ,$ the potential at the center of the cavity thus formed is: ($G=gravitational $ $constant$)

Question

From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R/2$ is removed, as shown in the figure. Taking gravitational potential $V=0$ at $r = \infty ,$ the potential at the center of the cavity thus formed is:
($G=gravitational $ $constant$)

${{ - 2GM} \over {3R}}$

${{ - 2GM} \over R}$

${{ - GM} \over {2R}}$

${{ - GM} \over R}$

Solution

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