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A cavity of radius R//2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R//2 from the centre of the sphere. The gravitational force on a particle of mass m at a distance R//2 from the centre of the sphere on the line joining both the centre of the cavity) [Here g=(GM)//R^(2), where M is the mass of the sphere |
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Answer» `(MG)/(2)` USING the FIGURE, F=Force due to whole sphere-Force due to cavity `F=(GMm)/(R^(3))-((R )/(2))-(G(M//8)m)/((R^(2)))` `=(GM m)/(R^(2))[(4)/(8)-(1)/(8)]=(3)/(8)(GM m)/(R^(2))=(3)/(8)mg` 
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