Question

The sum of magnitudes of two forces acting at a point is $16N$. If the resultant force is $8N$ and its direction is perpendicular to smaller force, then the forces are:

• A. $6N$ and $10N$
• B. $8N$ and $8/N$
• C. $4N$ and $12N$
• D. $2N$ and $14N$

Answer 1

The correct option is A $6N$ and $10N$

The correct answer is A.

Given,

The magnitude of two n forces is $16N$

The resultant force is $8N$

so,

$X+Y16(X<Y)$ and R is the resultant force perpendicular to X.

According to the Pythagoras theorem,

$\Rightarrow R^2=Y^2-X^2=(Y-X)(Y+X)=16(Y-X)$

$\Rightarrow (Y-X)=\frac{R^2}{(Y+X)}=\frac{8^2}{16}$

$\Rightarrow \frac{64}{16}=4$

$(Y+X)=16$ and $(Y-X)=4$

By solving a linear equation in two variable we get,

$Y=10N$ and $X=6N$