A solid sphere of mass M and radius a is surrounded by a uniform...

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 solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M

Options

A $\dfrac{GM}{9{a}^{2}}$
B $\dfrac{GM}{3{a}^{2}}$
C $\dfrac{2GM}{3{a}^{2}}$
D $\dfrac{2GM}{9{a}^{2}}$

Correct answer

B. $\dfrac{GM}{3{a}^{2}}$

Step-by-step solution

A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M

Gravitational field at point $P$ ,
$= \dfrac{GM}{{\left(3a\right)}^{2}} + \dfrac{G\left(2M\right)}{{\left(3a\right)}^{2}}$
$= \dfrac{GM}{9{a}^{2}} + \dfrac{2GM}{9{a}^{2}}$
$= \dfrac{GM}{3{a}^{2}}$

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