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Q.

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

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a

6 N and 10 N

b

8 N and 8 N

c

4N and12N

d

2N and 14N

answer is A.

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Detailed Solution

See figure

Question Image

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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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