The sum of magnitudes of two forces acting at a point is 16 N and their resultant `8N` is at `90^(@)` with the force of smaller magnitude. The two forces (in N) are

Options

A. a)11, 5
B. b)9, 7
C. c)6, 10
D. d) 2, 14

Answer

D

Explanation

Accoding to questions,
`P+Q=16impliesP=16-Q`
and resultant
`R=sqrt(P^(2)+Q^(2)+2PQcostheta)`
`8sqrt(3)=sqrt(P^(2)+Q^(2)+2PQcostheta)`
`tan90^(@)=(sintheta)/(P+Qcostheta)`
`P+Qcostheta=0`
`costheta=-(P)/(Q)`
`therefore 8sqrt(3)=sqrt(P^(2)+Q^(2)+2PQ(-(P)/(Q)))`
`=sqrt(P^(2)+Q^(2)-2P^(2))`
`8sqrt(3)=sqrt(Q^(2)-P^(2))`
`Q^(2)-P^(2)=192`
`Q^(2)-(Q-16)^(2)=192`
`Q^(2)-Q^(2)-256+32Q=192`
`32Q=192+256`
`Q=14`
`therefore P=2`