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 equiilbrium conditions, `sumF_(x)=0`
`Rightarrow F_(1)+1sin 45^(@)-2sin45^(@)=0`
`or F_(1)=2sin 45^(@)-1sin45^(@)=(2)/(sqrt(2))-(1)/(sqrt(2))=(2-1)/(sqrt2)=(1)/(sqrt2)N`
`and sumF_(y)=0 Rightarrow 1 cos45^(@)+2sin45^(@)-F_(2)=0`
`F_(2)=(2)/(sqrt2)+(1)/(sqrt2)=(2+1)/(sqrt2)=(3)/(sqrt2)N`