question_answer

Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is                        [Kerala PET 2005]

A)             \[-\sqrt{32}\frac{GM}{L}\]

B)               \[-\sqrt{64}\frac{GM}{{{L}^{2}}}\]

C)             Zero    

D)             \[\sqrt{32}\frac{GM}{L}\]

Correct Answer: A

Solution :

    Potential at the centre due to single mass = \[\frac{-GM}{L/\sqrt{2}}\] Potential  at the centre due to all four masses = \[-4\frac{GM}{L/\sqrt{2}}\] \[-4\sqrt{2}\frac{GM}{L}\] \[=-\sqrt{32}\times \frac{GM}{L}.\]