Question

The magnitude of two forces acting at a point is 16N.If the resultant force is 8N and its direction is perpendicular to the.samller force,then the forces are.

Answer 1

let A and B are two forces acting at a point . A< B
A + B = 16 ------(1)

question ask
A( A + B) = 0
A² = - A.B

A.B = -A² -----(2)

| A + B | = 8
√(A² + B² + 2A.B) = 8

√( A² + B² -2A²) = 8 from eqn (2)

( B² - A²) = 64
(B + A )( B - A) = 16
16 ( B - A ) = 64

B - A = 4 --------(3)

from eqn (1) and (3)

B = 10N and A = 6N