A solid sphere is of density J and radius R . The gravitational field at a distance R from the centre of the sphere, when r

Question

A solid sphere is of density J and radius R . The gravitational field at a distance R from the centre of the sphere, when r < R is: (A) (J λ G R3/r) (B) (4 λ G J r2/3) (C) (4 λ G J R2/3 r2) (D) (4 λ G J r/3)

Tardigrade Admin · Accepted Answer

Intensity I=(G M r/R3) =(G r/R3)((4/3) π R3 J) =(4 λ G r J/3)

Q. A solid sphere is of density $J$ and radius $R .$ The gravitational field at a distance $R$ from the centre of the sphere, when $r < R$ is:

$\frac{J λ G R ^{3}}{r}$

$\frac{4 λ G J r ^{2}}{3}$

$\frac{4 λ G J R ^{2}}{3 r ^{2}}$

$\frac{4 λ G J r}{3}$

Intensity $I = \frac{GM r}{R ^{3}}$
$= \frac{G r}{R ^{3}} (\frac{4}{3} π R^{3} J)$
$= \frac{4 λ G r J}{3}$

Q. A solid sphere is of density J and radius R. The gravitational field at a distance R from the centre of the sphere, when r<R is:

rJλGR3​

34λGJr2​

3r24λGJR2​

34λGJr​