Q.

The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?

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a

12,6

b

14,4

c

5, 13

d

10,8

answer is C.

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Detailed Solution

We have, P + Q = 18and R= 12Qsinθ=P and Qcosθ=RSquaring and adding, we getP2 +R2 = Q2or Q2 - P2 = R2 = 144Solving Eqs. (i) and (ii) , we getP = 5 and Q = 13.
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The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?