Three point masses 'm' each are kept at three verties of a square pf side 'a' as shown in figure. Find gravitation potential and field strength at point O.
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Answer

A, B, D

Explanation

Gravitational potential is a scalar quantity.
`:. V_o =` scalar sum of potentials sue to point massses at A, B, C,
`= -(Gm)/(a)-(Gm)/(sqrt(2a))-(Gm)/(a)`
`= -(Gm)/(a)[2+(1)/(sqrt2)]`
Gravitational field strength is a vector quantity. So, net field strength at O is the vector sum of three field strength produced due to three point masses at A, B, and.

Field strength due to A= field strength due to `C = (Gm)/(a^(2))` (towards to point masses )
`= E`(say)
Field strength due to `B = (Gm)/(sqrt2a)^(2) = (Gm)/(2a^2) = (E)/(2)`
Resultant of E and E is `sqrt(2)E` towards B.
`(E)/(2)` is also towards B.
`:. E_("net") = sqrt(2)E+(E)/(2) = (sqrt( 2)+(1)/(2)) E`
`(sqrt (2)+(1)/(2))(Gm)/(a^(2))` (towards B)