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

Options

A. 12 N, 6N
B. 13 N, 5 N
C. 10 N, 8N
D. 16 N, 2N

Answer

B

Explanation

Resultant R is perpendicular to smaller force P and (Q+P) = 18 N
`:. Q^(2) = P^(2) +R^(2) ` by right angled triangle
or `(Q^(2) -P^(2) )=R^(2)`
or `(Q+P) (Q-P)=R^(2)`
or `(18) (Q-P) = (12)^(2) `
or `(Q-P) = 8`
Hence Q = 13 N and P = 5 N