Four point masses are placed at the four corners of a square with masses m, 2m, 3m, and 4m (one at each corner). When the positions of m and 2m are interchanged, which of the following statements is correct?

gravitational field strength at centre will increase
gravitational field strength at centre will decrease
gravitational potential at centre will remain unchanged
gravitational potential at centre will decrease

Correct answer: gravitational potential at centre will remain unchanged

Solution

Gravitational potential is a scalar proportional to the sum of all masses divided by their equal distances from the center, so interchanging any two masses leaves the total sum unchanged and the potential constant.

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