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Question
Two concentric spherical shells have masses M1, M2 and radii R1, R2 (R1 < R2). What is the force exerted by this system on a particle of mass m1 if it is placed at a distance (R1+ R2)/2 from the centre?
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Solution
Consider that mass m is at a distance \[\frac{R_1 + R_2}{2}\] as shown in the figure.
The gravitational force of m due to the shell of M2 is zero, because the mass is inside the shell.
∴ Gravitational force due to the shell of mass M2 = \[\frac{G M_1 m}{\left( \frac{R_1 + R_2}{2} \right)^2} = \frac{4G M_1 m}{\left( R_1 + R_2 \right)^2}\]
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