The sum of magnitudes of two forces acting at a point is 16N. If the resultant force is 8N and its direction is perpendicualr to smaller force, then the forces are:

Options

A. `6N` and `10N`
B. `8N` and `8N`
C. `4N` and `12N`
D. `2N` and `14N`

Answer

A

Explanation

Let forces be A and B and `B lt A` then `A+B=16`

`A cos theta=R=8` and `A sin theta=B`
`rArr A^(2)=8^(2)+B^(2) " " rArr A^(2)-B^(2)=64`
`rArr (A-B)(A+B)=64 " " rArr A-B=4`
`rArr A=10N & B=6N`