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Question

Two concentric spherical shells have masses M1 and M2 and radii R1 and R2 (R1<R2). What is the force exerted by this system on a particle of mass m if it is at a distance (R1+R2)2 from the centre?

A
4G(M1+M2)m(R1+R2)2
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B
4GM2m(R1+R2)2
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C
4GM1m(R1+R2)2
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D
4G(M1M2)m(R1+R2)2
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Solution

The correct option is C 4GM1m(R1+R2)2

Field due to a spherical shell at an inside point is zero. Hence the field at the point P will be only due to M1.

So, the gravitational field at point P,

Eg=4GM1(R1+R2)2

Thus, the force on mass m is given by:

F=mEg

Substituting the value of Eg,

F=4GM1m(R1+R2)2

Hence, option (c) is correct.
Why this question: It is absolutely important to be well versed with the field due to a solid sphere and a hollow sphere both inside and outside. The concept is extremely important from a JEE standpoint.


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