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The sum of magnitudes of two forces acti...

The sum of magnitudes of two forces acting at a point is 16N. If the resultant force is 8N and its direction is perpendicualr to smaller force, then the forces are:

A

6N & 10N

B

8N & 8N

C

4N & 12N

D

2N & 14N

Text Solution

Verified by Experts

The correct Answer is:
1
`F_1 + F_2 = 16 " "`...(i)
`8= sqrt(F_1^(2) + F_2^(2) + 2F_1F_2 cos theta) `
`rArr F_1^(2) + F_2^(2) + 2F_1F_2 cos theta = 64 " "` …(ii)

`tan alpha = (F_2sin theta)/(F_1 + F_2 cos theta) = tan 90^(@) = oo`
`F_2 cos theta = -F_1" "` ...(iii)
Solving (i), (ii) and (iii) `rArr F_1 = 6N, F_2 = 10N`
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