question_answer

Two particle of mass m are placed at surface and centre of a shell of radius 2r and same mass m. Find the gravitation potential at a distance r from centre inside the sphere -

A) \[-\frac{Gm}{r}\]                       

B) \[-\frac{5}{2}\frac{Gm}{r}\]

C) \[-\frac{3}{2}\frac{Gm}{r}\]                  

D) None of these

Correct Answer: B

Solution :

\[V=-\frac{Gm}{r}-\frac{Gm}{2r}-\frac{Gm}{2r-r}\] \[=-\frac{Gm}{r}-\frac{Gm}{2r}-\frac{Gm}{r}\] \[=-\frac{2Gm}{r}-\frac{Gm}{2r}\] \[=-\frac{Gm}{r}\left( 2+\frac{1}{2} \right)=-\frac{5}{2}\,\frac{Gm}{r}\]