question_answer

A particle of mass M is situated at the centre of spherical shell of mass and radius a. The magnitude of the gravitational potential at a point situated at \[\frac{a}{2}\] distance from the centre, will be  

A) \[\frac{2GM}{a}\]           

B) \[\frac{3GM}{a}\]           

C) \[\frac{4GM}{a}\]           

D) \[\frac{GM}{a}\]

Correct Answer: B

Solution :

\[{{V}_{p}}={{V}_{sphere}}+{{V}_{partical}}\]                                 \[{{V}_{p}}=\frac{GM}{a}+\frac{GM}{a/2}\]                                 \[V=\frac{GM}{a}+\frac{2GM}{a}\]                                 \[{{V}_{p}}=\frac{3GM}{a}\]