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Gravitation question

2011 · Q101
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Gravitation question

2011 · Q101

NEETPhysicsGravitationMCQ+4 / −1
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 :
  1. A
    GMa{{GM} \over a}aGM​
  2. B
    2GMa{{2GM} \over a}a2GM​
  3. C
    3GMa{{3GM} \over a}a3GM​
  4. D
    4GMa{{4GM} \over a}a4GM​
View written solutionFree

Correct answer: C

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

V1=−GMa/2{V_1} = - {{GM} \over {a/2}}V1​=−a/2GM​

Gravitational potential at point P due to spherical shell is

V2=−GMa{V_2} = - {{GM} \over a}V2​=−aGM​

Hence, total gravitational potential at point P is V = V1 + V2

=−GMa/2+(−GMa)=−2GMa−GMa=−3GMa = - {{GM} \over {a/2}} + \left( { - {{GM} \over a}} \right) = - {{2GM} \over a} - {{GM} \over a} = - {{3GM} \over a}=−a/2GM​+(−aGM​)=−a2GM​−aGM​=−a3GM​

∣V∣=3GMa\left| V \right| = {{3GM} \over a}∣V∣=a3GM​

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