Three equal point masses of each mass m are located, respectively at three corners of a square of edge length l as shown in figure. The magnitude of intensity of gravitational field (g) at the fourth corner due to these masses is

Options

A. `(Gm)/(l^(2))((sqrt2+2)/(2))`
B. `(2Gm)/(l^(2))((1+sqrt2))/(sqrt2)`
C. `(Gm)/(l^(2))((2sqrt2+1)/(2))`
D. `(Gm)/(l^(2))(sqrt2+1)/(2)`

Answer

c

Explanation

`E_(1)=(GM)/(l^(2)), E_(2)=(GM)/(l^(2)), and E_(3)=(GM)/(2l^(2))`
`E_(R)=sqrt((E_(1)^(2)+E_(2)^(2))`
`=sqrt(((GM)/(l^(2)))^(2)+((GM)/(l^(2))))=sqrt2((GM)/(l^(2)))`
`E'_(R)=E_(R)+E_(3)=(GM)/(l^(2))(sqrt2+(1)/(2))`