Question

four identical point masses each equal to M are placed at four corners of a square of side. calculate the force of attraction on another point mass M1 kept at the centre of the square.
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Answer 1

Side of square = a

Distance from M1, r = a/root2

F = GM1M/r^1/2

Add vectorially... By symmetry net force is zero

Answer 2

Force of attraction on another point mass M1 kept at the centre of the square is ZERO

• The given masses are ideal point masses and do not exhibit any electrical characters, we are free to use Newton’s Law of Gravity.
• The force of attraction between the 4 bodies placed at the boundary and the lone mass placed at the centre can be given by the application of the following formula 4 times:

                      $F =  \frac{(GMM1)}{(r^2)}$

Where, G is universal gravitational constant and r is the distance     between the central mass and boundary mass.

• Since each mass exerts the above force which nullifies each other
• The combined force felt by the central mass will be:

                                     F =  0