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Question: Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the posit...

Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position where the gravitational field due to them is zero is V, then

A

V=−Gd(m+M)V = - \frac { G } { d } ( m + M )

B

V=−GmdV = - \frac { G m } { d }

C

V=−GMdV = - \frac { G M } { d }

D

V=−Gd(m+M)2V = - \frac { G } { d } ( \sqrt { m } + \sqrt { M } ) ^ { 2 }

Answer

V=−Gd(m+M)2V = - \frac { G } { d } ( \sqrt { m } + \sqrt { M } ) ^ { 2 }

Explanation

Solution

If PP is the point of zero intensity, then

d−x=mM+mdd - x = \frac { \sqrt { m } } { \sqrt { M } + \sqrt { m } } d

Now potential at point P, V=V1+V2V = V _ { 1 } + V _ { 2 } =−GMx−GMd−x= - \frac { G M } { x } - \frac { G M } { d - x }

Substituting the value of x and d – x we get V=−Gd(m+M)2V = - \frac { G } { d } ( \sqrt { m } + \sqrt { M } ) ^ { 2 }.