From a solid sphere of mass


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

  1. $\frac{-2 \mathrm{GM}}{3 \mathrm{R}}$

  2. $\frac{-2 \mathrm{GM}}{\mathrm{R}}$

  3. $\frac{-\mathrm{GM}}{2 \mathrm{R}}$

  4. $\frac{-\mathrm{GM}}{\mathrm{R}}$

Correct Option: , 4


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