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JEE Main 2019 (9 Apr, Shift 1) · Gravitational Field

Gravitational Field question from JEE Main 2019 (9 Apr, Shift 1)

Q11JEE Main 2019 · 9 APR · SHIFT 1Medium

Gravitational Field

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be:

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Answer: (a)

The shell extends from $a$ to $3a$ , so at $r = 3a$ the whole mass $M + 2M = 3M$ is enclosed.
Enclosed mass acts as a point mass at the centre: $E = \frac{G(3M)}{(3a)^2}$
$E = \frac{3GM}{9a^2} = \frac{GM}{3a^2}$
So the answer is (a) $\frac{GM}{3a^2}$ .

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