Gravitational Field question from JEE Main 2013 (9 Apr, Shift 1)

Answer: (c)

1. Removed sphere has radius $\frac{R}{2}$, so its mass is $\frac{M}{8}$ (mass $\propto$ volume $\propto r^3$).
2. For a very far point, both the full sphere and the removed part act as point masses at distance $\approx x$.
3. $E = \frac{GM}{x^2} - \frac{G(M/8)}{x^2} = \frac{7}{8}\frac{GM}{x^2}$
4. So the answer is (c) $\frac{7}{8}\frac{GM}{x^2}$.