Question

18N nd their resultant is perpendicular to the smaller force nd magnitude of resultant is 12N.Then the magnitudes of the forces are

1)12N,6N
2)13N,5N
3)10N,8N
4)16N,2N

If u know the answer then only answer it otherwise leave it

Answer 1

Let A and B be two forces, A is greater than B

Resultant = A + B is perpendicular to B

so the dot product of (A + B) and B will be equal to 0

(A + B). B = 0

A.B + B2 = 0

AB cos(theta) + B2 = 0

2AB cos(theta) = -2B2

-

R2 = A2 + B2 + 2AB cos(theta)

substitute the value of R and 2AB cos(theta)

122 = A2 + B2 - 2B2

A2 - B2 = 144

(A - B)(A + B) = 144

(A - B x 18 = 144

A - B = 144/18 = 8

A + B = 18 and A - B = 8

Therefore A = 13 N , B = 5 N