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Newton's Law of Gravitation

Two concentri...

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

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