Question 414: Gravitation

Question

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :

Accepted Answer

Here, Mass of a particle = M
Mass of a spherical shell = M
Radius of a spherical shell = a
Let O be centre of a spherical shell.
Gravitational potential at point P due to particle at O is
$${V_1} =  - {{GM} \over {a/2}}$$
Gravitational potential at point P due to spherical shell is
$${V_2} =  - {{GM} \over a}$$
Hence, total gravitational potential at point P is  V = V
1
+ V
2
$$ =  - {{GM} \over {a/2}} + \left( { - {{GM} \over a}} \right) =  - {{2GM} \over a} - {{GM} \over a} =  - {{3GM} \over a}$$
$$\left| V \right| = {{3GM} \over a}$$

Answer

$${{GM} \over a}$$

Answer

$${{2GM} \over a}$$

Answer

$${{3GM} \over a}$$

Answer

$${{4GM} \over a}$$

Gravitation

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :

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