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 `12 N`
D. `2 N` and `14 N`

Answer

A

Explanation

`P + Q = 16 , R = 8 , let P lt Q`
`R^(2) = P^(2) + Q^(2) + 2PQ cos theta`
` (8)^(2) = P^(2) + (16 - P)^(2) + 2 PQ cos theta` (i)
`tan 90^(@) = ( Q sin theta)/( P + Q sin theta)`
`(1)/(0) = (Q sin theta)/(P + Q cos theta)`
`P + Q cos theta = 0 rArr Q cos theta = -P in (i)`
`64 = P^(2) + ( 16 - P)^(2) + 2P (-P)`
`= P^(2) + 256 + P^(2) - 32 P - 2P^(2)`
`32 P = 192 rArr P = 6 N , Q = 10 N`