Question

The greatest and least resultant of two forces acting at a point is $10N$ and $6N$ respectively. If each force is increased by $3N$, find the resultant of new forces when acting at a point at an angle of ${90}^{\circ }$ with each other.

Answer 1

Let $A$ and $B$ be the two forces,
Greatest resultant $=A+B=10$ ... (i)
Least resultant $=A-B=6$ ... (ii)
Solving (i) and (ii), we get, $A=8N$ and $B=2N$.
When each force is increased by $3N$ then
$A^{\prime }=A+3=8+3=11N$, then
$B^{\prime }=B+3=2+3=5N$
As the new forces are acting at an angle of ${90}^o$ (i.e., $\theta ={90}^o)$
So $R^{\prime }=\sqrt{A^{\prime 2}+B^{\prime 2}}=\sqrt{(11{)}^2+(5{)}^2}=\sqrt{146}N$