Question

The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is
perpendicular to minimum force then the force are
(A) 6 N and 10 N (B) 8 N and 8 N (C) 4 N and 12 N (D) 2 N and 14 N

Answer 1

Explanation:

the magnitude of larger force be (16 - x) Newton, as their sum is 16 N. And, the magnitude if larger force is given by, (16 - x) = (16 - 6) = 10N. Hence, the smaller force is 6N and the larger force is 10N.

Answer 2

CORRECT ANSWER OF YOUR QUESTION IS (A) 6N AND 10N

Let the magnitude of lesser force be x Newton. So, the magnitude of larger force be (16 - x) Newton, as their sum is 16 N.

And it is given that, the resultant force is 8N which is perpendicular to lesser force, i.e., x Newton,

So,

(16 - x)² = x² + 8²

= (16)² + (x)² - 2 * 16 * x = x² + 64

= 256 - 32x = 64

= 32x = 256 - 64

= 32x = 192

= x = 6

Therefore,

The magnitude of lesser force = x = 6 N

And, the magnitude if larger force is given by, (16 - x) = (16 - 6) = 10N.

Hence, the lesser force is 6N and the larger force is 10N.