First slide

Vectors

Question

The sum of magnitudes of two forces acting at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N, then the force are

Moderate

A

6 N and 10 N
B

8 N and 8 N
C

4N and12N
D

2N and 14N

Solution

See figure
Given P+Q=16N ...(1)
Here R is normal to P, i.e.,
R² = Q² -P² =(Q -P)(Q+P)
or (8)² = (Q - P) (16)
$∴ Q - P = 4 . . . . (2)$
From eqs. (1) and (2)
P=6N and Q=10N

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