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A solid sphere of uniform density and radius applies a gravitational force of attraction equal to on a particle placed at , distance from the centre of the sphere. A spherical cavity of the radius is now made in the sphere as shown in the figure. The sphere with cavity now applied a gravitational force on the same particle placed at . The ratio will be

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The correct answer is:
Gravitational force due to solid sphere,
where and are mass of the solid sphere and particle respectively and is the radius of the sphere. The gravitational force on particle due to sphere with cavity = force due to solid sphere creating cavity, assumed to be present above at that position
i.e.,
So,
where and are mass of the solid sphere and particle respectively and is the radius of the sphere. The gravitational force on particle due to sphere with cavity = force due to solid sphere creating cavity, assumed to be present above at that position
i.e.,
So,
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