Question

A solid sphere of mass M and radius R has a spherical cavity of radius R 2 such that the centre of cavity is at a distance R 2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R 4 from the centre of sphere.
The gravitational force on mass m is

(a) 11 G M m R 2 (b) 14 G M m R 2 (c) G M m 2 R 2 (d) G M m R 2

Answer 1

Explanation:

Given A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R/2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R/4 from the centre of sphere.

The gravitational force on mass m is

•    In a sphere there is a spherical cavity of radius R/2 . A point mass is placed inside cavity at a distance R/4.
• So gravitational field is constant.
• So E at centre will be  
• Ec = ET – ER
•     = GM / R^3 (R/2) – 0 (0 because cavity at centre)
• Ec = GM / 2 R^2    

Force will be F = GMm / 2R^2    

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