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

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Solution

The correct option is A

Potential due to a point mass M at a distance r is $\frac{- G M}{r}$
Potential at the centre due to single mass = $\frac{- G M}{\frac{L}{\sqrt{2}}}$
Potential at the centre due to all four masses
$= - 4 \sqrt{2} \frac{G M}{L} = - \sqrt{32} \times \frac{G M}{L}$

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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

The correct option is A Potential due to a point mass M at a distance r is −GMr Potential at the centre due to single mass = −GML√2 Potential at the centre due to all four masses =−4√2GML=−√32×GML

The correct option is A

Potential due to a point mass M at a distance r is $\frac{- G M}{r}$
Potential at the centre due to single mass = $\frac{- G M}{\frac{L}{\sqrt{2}}}$
Potential at the centre due to all four masses
$= - 4 \sqrt{2} \frac{G M}{L} = - \sqrt{32} \times \frac{G M}{L}$