The resultant ot two forces acting at an angle of ` 150^@` is ` 10 N` and is perpendicular to one of the forces. The other force is .

Options

A. `20 // sqrt 2 N`
B. `10 // sqrt 3 N`
C. ` 20 N`
D. ` 20 sqrt 3 N`

Answer

C

Explanation

` 10^@ = A^2 + b^2 +2 AB cos 150^@`
` = A^2 +b^2 - 2 AB ( sqrt 3 //2)` …(i)
` tan 90^@ = ( B sin 150^@)/( A+ B cos ` 15^@) =0`
or ` A+B cos 1 50^@ =0`
or ` A= B xx sqrt 3//3` …(ii)
` From (i), ` 100 = 3/ 4 B^2 + B^@ - ( 3 B^2)/2 = B^2/4`
` or ` B = 20 N`.