The density inside a solid sphere of radius a is given by 
, where 
is the density ast the surface and r denotes the distance from the centre. Find the graittional field due to this sphere at a distance 2a from its center.
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Sol. The field is required at a point outside the sphere. Dividing the sphere in concentric shells,
each = shell can be replaced by a point particle at its center having mass equal to the mass of the shell. Thus the whole sphere can be replaced by a point particle at its center having mass equal to the mass of the given sphere. If the mass of the sphere is M the gravitation N/Al field at the given point is
The mass M may be calculated as follows. Consider a concentric shell of radius r and thickness dr. Its volume is
and its mass is
The mass of the whole sphere is
Thus by i the gravitation N/Al field is
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