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Gravitational Field Due to a Solid Sphere

Two concentri...

Question

Two concentric shells of uniform density having masses $M_{1}$ and $M_{2}$ are situated as shown in figure. Then, the force on a particle of mass m when the particle is located at $r = a$ is

G (M_{1} - M_{2}) \frac{m}{a^{2}}

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G (M_{1} + M_{2}) \frac{m}{a^{2}}

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G M_{1} \frac{m}{a^{2}}

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G M_{2} \frac{m}{a^{2}}

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Solution

The correct option is B $G (M_{1} + M_{2}) \frac{m}{a^{2}}$
Given that the mass m is kept at distance a from the centre of both spherical shells $M_{1}, M_{2}$
Consider the force due to $M_{1}$ as $F_{1}$
so, $F_{1} = \frac{G M_{1} m}{a^{2}}$
Similarly $F_{2} = \frac{G M_{2} m}{a^{2}}$
total foce is given by $F_{1} + F_{2} = \frac{G M_{1} m}{a^{2}} + \frac{G M_{2} m}{a^{2}} = G (M_{1} + M_{2}) \frac{m}{a^{2}}$

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