Question

# 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

A
32GML
B
64GML2
C
zero
D
32GML

Solution

## The correct option is A $$-\sqrt{32}\cfrac{GM}{L}$$$${ \mu }_{ p }={ \mu }_{ 1p }+{ \mu }_{ 2p }+{ \mu }_{ 3p }+{ \mu }_{ 4p }$$     $$=\dfrac { -GM }{ L/\sqrt { 2 } } -\dfrac { GM }{ L/\sqrt { 2 } } -\dfrac { GM }{ L/\sqrt { 2 } } -\dfrac { GM }{ L/\sqrt { 2 } }$$     $$=\dfrac { -1 }{ L/\sqrt { 2 } }$$ $$(GM+GM+GM+GM)$$ $$=\dfrac { -4GM }{ L/\sqrt { 2 } } =\dfrac { -4\sqrt { 2 } GM }{ L }$$Physics

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