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 ${90}^0$ with the force of smaller magnitude, what are the, magnitudes of forces

• A. $12,5$
• B. $14,4$
• C. $5,13$
• D. $10,8$

Answer 1

The correct option is C $5,13$

Let the magnitude of smaller force is $P$, the magnitude of larger force is $Q$ and the resultant force is $R$.

As the resultant force makes ${90}^{\circ }$ with the smaller force $P$ then $Q$ forms the hypotenuse of the triangle.

Thus, it can be written as,

$Q^2-P^2=R^2$

$Q^2-P^2={\left(12\right)}^2$

$Q^2-P^2=144$ (1)

The sum of magnitudes of two forces is given as,

$P+Q=18$

$Q=18-P$ (2)

Substituting the value from equation (2) in equation (1), we get

${\left(18-P\right)}^2-P^2=144$

$P=5N$

Substituting the value of $P$ in equation (1), we get

$Q=18-5$

$=13N$

Thus, the magnitude of the forces are $5N$ and $13N$.