Question

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

• A. gravitational field strength at centre will increase
• B. gravitational field strength at centre will decrease
• C. gravitational potential at centre will remain unchanged
• D. gravitational potential at centre will decrease

Answer 1

Answer: (A), (C)

The correct options are
A gravitational field strength at centre will increase
C gravitational potential at centre will remain unchanged

$E=\frac{Gm}{r^2}$

$E_{net}^{\prime }=2\sqrt{2}E=\frac{2\sqrt{2}Gm}{r^2}$

$E_{net}^{\prime }=\sqrt{{\left(9E\right)}^2+E^2}$

$=\sqrt{10}E$

$=\frac{\sqrt{10}Gm}{r^2}$

$E_{net}^{\prime }>E_{net}$

Potential in both cases is

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

$=-\frac{10Gm}{r}$