At a point the addition of two active force is $18 N$ . If the magnitude of resultant is $12 N$ and meet at right angle. Then, magnitude of forces are

5 N, 13 N

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6 N, 12 N

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8 N, 10 N

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None of these

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Solution

The correct option is A $5 N, 13 N$
Let the forces be $P$ and $Q$ such that $(P > Q)$ and $O A C B$ be a parallelogram, then
$P + Q = 18 . . . . (i)$
From figure
$A C^{2} = O A^{2} + O C^{2}$
$\Rightarrow Q^{2} = P^{2} + 144$
$\Rightarrow Q^{2} - P^{2} = 144 . . . . (i i)$
Solving Eqs. (i) and (ii), we get
$P = 5 N, Q = 13 N$ .

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At a point the addition of two active force is 18 N. If the magnitude of resultant is 12 N and meet at right angle. Then, magnitude of forces are

The correct option is A 5 N,13 NLet the forces be P and Q such that (P>Q) and OACB be a parallelogram, thenP+Q=18....(i)From figureAC2=OA2+OC2⇒Q2=P2+144⇒Q2−P2=144....(ii)Solving Eqs. (i) and (ii), we getP=5N,Q=13N.

At a point the addition of two active force is $18 N$ . If the magnitude of resultant is $12 N$ and meet at right angle. Then, magnitude of forces are