Two equal forces are acting at a point with an angle of `60^(@)` between them. If the resultant force is equal to `40sqrt3` N, the magnitude of each force is

Options

A. 40N
B. 20N
C. 80N
D. 30N

Answer

A

Explanation

`R= sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1) F_(2) cos theta)`
Since, `F_(1)= F_(2)= F " & " theta= 60^(@)`
`rArr 40 sqrt3 = sqrt(2F^(2) + 2F^(2) cos 60^(@))= sqrt(3F^(2))`
`rArr 40 sqrt3= F sqrt3`
`rArr F= 40N`