Question

Two forces are such that the sum of their magnitudes is 18N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitude of the forces are
A. (a) 12N, 6N
B. (b) 13N, 5N
C. (c) 10N, 8N
D. (d) 16N, 2N

Answer 1

Correct Answer - B
Let the two forces be `F_1` and `F_2` and let `F_2ltF_1`. R is the resultant force.
Given `F_1+F_2=18` …(i)
From the figure `F_2^2+R^2=F_1^2`
`F_1^2-F_2^2=R^2`
`:.` `F_1^2-F_2^2=144`
Only option (b) follows equation (i) and (ii).