First slide

Scalars and Vectors

Question

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

Moderate

A

12, 5
B

14, 4
C

5, 13
D

10, 8

Solution

Let P be the smaller force and Q be the greater force, then according to the problem
$\begin{array}{l} P + Q = 18 . . . . . . . . . . . . . . . . . . (i) \end{array}$
$P^{2} + R^{2} = Q^{2}$
$\Rightarrow R^{2} = Q^{2} - P^{2}$
$\Rightarrow 12^{2} = (Q - P) (Q + P)$
$\Rightarrow 144 = (Q - P) 18$
$\Rightarrow (Q - P) = 8 - - - - (2)$
$\begin{array}{l} f r o m (1) & (2) w e g e t \\ Q + P = 18 \\ Q - P = 8 \\ _ \\ 2 Q = 26 \\ \\ Q = 13 \\ s u b s t i t u t e i n (1) w e g e t \\ P = 5 \end{array}$

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