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(C) For a point at a distance $y$ from the center of a uniform sphere of density $\rho$,the gravitational force $F$ acting on a body of mass $m$ is du

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$\frac{4}{3} \pi G \rho y$

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(C) For a point at a distance $y$ from the center of a uniform sphere of density $ho$,the gravitational force $F$ acting on a body of mass $m$ is due only to the mass $M'$ contained within a sphere of radius $y$.$M' = 	ext{Volume} 	imes 	ext{Density} = \left(\frac{4}{3} \pi y^3ight) ho$.According to Newton's law of gravitation,the force is $F = \frac{G M' m}{y^2}$.Substituting $M'$,we get $F = \frac{G m}{y^2} \left(\frac{4}{3} \pi y^3 hoight) = \frac{4}{3} \pi G ho m y$.Since $F = ma$,the acceleration $a$ is given by $a = \frac{F}{m} = \frac{4}{3} \pi G ho y$.

Suppose a vertical tunnel is dug along the diameter of the Earth,which is assumed to be a sphere of uniform mass having density $\rho$. If a body of mass $m$ is dropped into this tunnel,its acceleration at a distance $y$ from the center is given by

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