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Four point masses are plaaced at four co...

Four point masses are plaaced at four corners of a square as shows. When positions of `m `and `2m` are interchanged

A

gravitational field strength at centre will increases

B

gravitational field strength at centre will decreases

C

gravitational potential at centre will remain unchanged

D

gravitational potential at centre will decrease

Text Solution

Verified by Experts

The correct Answer is:
A, C
`E = (Gm)/(r^(2))`

`E'_(net) = 2sqrt(2) E = (2 sqrt(2) Gm)/(r^(2))`
`E'_("net") = sqrt((9E)^(2) + E^(2)) = sqrt(10) E`
`= (sqrt(10)Gm)/(r^(2))`
`E'_("net") gt E_("net")`

Potential in both cases is
`V_(net) = - (G)/(r ) (m + 2m + 3m+ 4m)`
`= - (10 Gm)/(r )`
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