There are four force acting at a point `p` produced by strings as shown in figure, which is at rest. The force `F_(1)` and `F_(2)` are .

Options

A. `(1)/(sqrt2)N, (3)/(sqrt2)N`
B. `(3)/(sqrt2)N, (1)/(sqrt2)N`
C. `(1)/(sqrt2)N, (1)/(sqrt2)N`
D. `(3)/(sqrt2)N, (3)/(sqrt2)N`

Answer

A

Explanation

Applying equilibrium conditios,
`sumF_(x)=0`
implies `F_(1)+1sin45^(@)-2sin45^(@)=0`
or `F_(1)=2sin45^(@)-1sin45^(@)`
`=(2)/(sqrt(2))-(1)/(sqrt(2))=(2-1)/(sqrt(2))=(1)/(sqrt(2))N`