Q. A solid sphere is of density $\rho$ and radius $R$. The gravitational field at a distance $r$ from the centre of the sphere, where $r < R$, is
A) $\frac{\rho\pi GR^{3}}{r}$
B) $\frac{4\pi G\rho r^{2}}{3}$
C) $\frac{4\pi G\rho R^{3}}{3r^{2}}$
D) $\frac{4\pi G\rho r^{\ }}{3}$
Explanation
(d) When $r < R$, Gravitational field intensity,
$I = \frac{GM}{R^{3}}r = \frac{Gr}{R^{3}}\left( \frac{4}{3}\pi R^{3}\rho \right) = \frac{4\pi G\rho r}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.