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The sum of the magnitudes of two forces ...

The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at `90^(@)` with the force of smaller magnitude, What are the magnitudes of forces?

A

12, 5

B

14, 4

C

5, 13

D

10, 8

Text Solution

Verified by Experts

The correct Answer is:
C
Let P be the smaller force and Q be the greater force,then according to problem
`P+Q=18`
`R=sqrt(p^(2)+Q^(2)+2PQcostheta)=12`
`tanphi=(Qsintheta)/(P+Qcostheta)=tan90=infty`
`P+Qcostheta=0`
By solving (i), (ii) and (iii) we will get `P=5` and `Q=13`
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