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Four point masses are placed at four corners of a square as shown. When positions of $m$ and $2 m$ are interchanged

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gravitational field strength at centre will increase

gravitational potential at centre will remain unchanged

gravitational potential at centre will decrease

gravitational field strength at centre will decrease

answer is A, C.

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Detailed Solution

$E = \frac{G m}{r^{2}}$

gravitational field strength at centre will increases

$E_{net}^{'} = 2 \sqrt{2} E = \frac{2 \sqrt{2} G m}{r^{2}}$

$E_{net}^{'} = \sqrt{(9 E)^{2} + E^{2}} = \sqrt{10} E$

$= \frac{\sqrt{10} G m}{r^{2}}$

Potential in both cases is

$V_{n e t} = - \frac{G}{r} (m + 2 m + 3 m + 4 m)$

$= - \frac{10 G m}{r}$

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