Question

The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are

• A. 13, 5
• B. 12, 6
• C. 14, 4
• D. 11, 7

Answer 1

Answer: (A)

13, 5

Answer 2

$P + Q = 18 , R = 12 , \theta = 90 ^ { \circ }$, (say)

$\tan \theta = \tan 90 ^ { \circ } = \infty$

$\Rightarrow P + Q \cos \alpha = 0$ , $\therefore \cos \alpha = \frac { - P } { Q }$

Also, $( 12 ) ^ { 2 } = P ^ { 2 } + Q ^ { 2 } + 2 P Q \cos \alpha$

or $144 = P ^ { 2 } + Q ^ { 2 } + ( 2 P ) ( - P )$

$\Rightarrow 144 = Q ^ { 2 } - P ^ { 2 } = ( Q + P ) ( Q - P )$

or $144 = 18 ( Q - P )$ or $Q - P = 8$

After solving Q = 13, P = 5.