The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N. If the smaller force is magnitude x, then the value of x is

Options

A. 13,5
B. 12,6
C. 10,6
D. 11,7

Answer

A

Explanation

We have, `|P|+|Q|=18N,|R|=|P+Q|+12N`
`alpha=90^(@)`
`P+Q cos theta=0`
`impliesQ cos theta=-P`
Now. `R^(2)=P^(2)+Q^(2)+2PQcostheta`
`impliesR^(2)+P^(2)+Q^(2)+2P(-P)=Q^(2)-P^(2)`

`implies12^(2)=(P+Q)(Q-P)=18(Q-P)`
`impliesQ-P=8 and Q+P=18`
`impliesQ=13,P=5`
`therefore` magnitude of two forces are 5 N and 13N.