A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :

Question

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be : (A) (2GM/9a2) (B) (GM/3a2) (C) (GM/9a2) (D) (2GM/3a2)

Tardigrade Admin · Accepted Answer

We use gauss's Law for gravitation g. 4 π r2 = (Mass enclosed) 4πG g = (3M4 π G/4 π (3a)2) = (MG/3a2) Option (2)

Q. A solid sphere of mass $^{'} M^{'}$ and radius $^{'} a^{'}$ is surrounded by a uniform concentric spherical shell of thickness $2 a$ and mass $2 M$ . The gravitational field at distance $^{'} 3 a^{'}$ from the centre will be :

$\frac{2 GM}{9 a ^{2}}$

$\frac{GM}{3 a ^{2}}$

$\frac{GM}{9 a ^{2}}$

$\frac{2 GM}{3 a ^{2}}$

We use gauss's Law for gravitation
$g .4 π r^{2}$ = (Mass enclosed) 4 $π$ G
$g = \frac{3 M 4 π G}{4 π ( 3 a ) ^{2}}$
$= \frac{MG}{3 a ^{2}}$
Option (2)

Q. A solid sphere of mass ′M′ and radius ′a′ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ′3a′ from the centre will be :

9a22GM​

3a2GM​

9a2GM​

3a22GM​