Two concentric spherical shells have masses M1- M2 and radii R1- R2 -R1 lt- 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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Standard X

Physics

Gravitational Potential Energy

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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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?

Consider that mass m is at a distance R1+R22 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 = GM1mR1+R222=4GM1mR1+R22

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?