Gravitational Field question from JEE Main 2017 (9 Apr, Shift 1)

Answer: (b)

1. Mass within $r \le R$: $M(r) = \int_0^r 4\pi r^2 \frac{k}{r} dr = 2\pi k r^2$
2. Inside: $a = \frac{GM(r)}{r^2} = 2\pi G k$, a constant.
3. Outside: $a = \frac{GM}{r^2}$, falls as $\frac{1}{r^2}$.
4. Flat line up to $R$, then a falling curve. So the answer is (b).