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Questions  >>  JEEMAIN and NEET  >>  Physics  >>  Class11  >>  Gravitation
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Q)

Mass density of a solid sphere is $\rho$. Radius of sphere is R. The gravitational field at a distance $r$ from the center of the sphere inside it is

\[(a)\;\frac{4 \rho G \pi r}{3} \quad (b)\;\frac{4 \rho G \pi r^2}{3} \quad (c)\;\frac{4 \rho G \pi R^3}{3r^2} \quad (d)\;\frac{ \rho G R^3}{\pi r} \]

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A)
Gravitational Potential energy at a distance r from center where $r \leq R$ is
$ E(r) =\large\frac{GM}{R^3} r$
$ \qquad =\large\frac{Gr}{R^3}\bigg(\frac{4}{3} $$ \pi R^3 \rho\bigg)$
$\qquad =\large\frac{4 G r \pi \rho}{3}$
Hence a is the correct answer. 

 

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