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Two concentric spherical shells have masses $M_{1}, M_{2}$ and radii $R_{1}, R_{2} (R_{1} < R_{2})$ , What is a force exerted by this system on a particle of mass $m_{1}$ if it is placed at a distance $(R_{1} + R_{2}) / 2$ from the centre?

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$\frac{4 G M_{1} m}{{(R_{1} + R_{2})}^{2}}$

$\frac{4 G M_{1} m}{(R_{1} + R_{2})}$

$\frac{4 G M_{2} m}{(R_{1} + R_{2})}$

$\frac{4 G M_{2} m}{{(R_{1} - R_{2})}^{2}}$

answer is A.

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Detailed Solution

The gravitational force on ‘m1’ due to the shell of M2 is 0(As the mass is inside the shell).

m1 is at a distance $\frac{R_{1} + R_{2}}{2}$

Then the gravitational force due tothe shell of M1 is given by

$= \frac{G M_{1} m}{{(\frac{R_{1} + R_{2}}{2})}^{2}} = \frac{4 G M_{1} m}{{(R_{1} + R_{2})}^{2}}$

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