Question 39 of 223

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:

A$\dfrac{GM}{9{a}^{2}}$B$\dfrac{GM}{3{a}^{2}}$C$\dfrac{2GM}{3{a}^{2}}$D$\dfrac{2GM}{9{a}^{2}}$

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Answer: (B) $\dfrac{GM}{3{a}^{2}}$

Gravitational field at point $P$,
$=\dfrac{GM}{{\left(3a\right)}^{2}}+\dfrac{G\left(2M\right)}{{\left(3a\right)}^{2}}$
$=\dfrac{GM}{9{a}^{2}}+\dfrac{2GM}{9{a}^{2}}$
$=\dfrac{GM}{3{a}^{2}}$