Physics - Gravitation Question with Solution | TestHub

Let mass of smaller sphere (which has to be removed) is $\mathrm{m}$ Radius $=\frac{\mathrm{R}}{2}($ from figure $)$ $$\begin{array}{rl}& \frac{\mathrm{M}}{\frac{4}{3}\pi {\mathrm{R}}^3}=\frac{\mathrm{m}}{\frac{4}{3}\pi {\left(\frac{\mathrm{R}}{2}\right)}^3}\\ & \Rightarrow \mathrm{m}=\frac{\mathrm{M}}{8}\end{array}$$ Mass of the left over part of the sphere $${\mathrm{M}}^{\prime }=\mathrm{M}-\frac{\mathrm{M}}{8}=\frac{7}{8}\mathrm{M}$$ Therefore gravitational field due to the left over part of the sphere $$=\frac{{\mathrm{GM}}^{\prime }}{{\mathrm{x}}^2}=\frac{7}{8}\frac{\mathrm{GM}}{{\mathrm{x}}^2}$$