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Archimedes' Principle

Two concentri...

Question

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

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Solution

The gravitational force on 'm' due to the shell of $M_{2}$ is 0.
m is at a distance $\frac{R_{1} + R_{2}}{2} .$
Tehn gravitational force due to M 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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