The sum of two forces at a point is 16N. if their resultant is normal to the smaller force and has a magnitude of 8N, then two forces are

Options

A. `6 N and 10 N`
B. `8 N and 8 N`
C. `4 N and 2 N`
D. `2 N and 14 N`

Answer

A

Explanation

`A+B= 16` (given)….(i)
`tan alpha=(B sin theta)/(A+B cos theta)= tan 90^(@)`
`:. A+B cos theta= 0impliescos theta= (-A)/B`.....(ii)
`8= sqrt(A^(2)+B^(2)2AB cos theta)`....(iii)
By solving equ.(i),(ii),(iii) we get
`A=6 N,B= 10 N`