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

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Solution

Since $R_{1} < R_{2} R_{1} < \frac{R_{1} + R_{2}}{2} < R_{2}$

Thus, the particle lies between two shells.

Hence, only force applied will be that due to inner shell.

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

Answer is $\frac{4 G m m_{1}}{{(R_{1} + R_{2})}^{2}}$ .

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Two concentric spherical shells have masses and radii m1,m2 and radii R1,R2(R1<R2). Calculate the force exerted by this system on a particle of mass m, if it is placed at a distance (R1+R2)2 from the centre.

Since R1<R2R1<R1+R22<R2Thus, the particle lies between two shells.Hence, only force applied will be that due to inner shell.F=Gm1m(R1+R22)2=4Gmm1(R1+R2)2Answer is 4Gmm1(R1+R2)2.

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