Question

The greatest and least resultant of two forces acting at a point are $10N$ 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 equations (i) and (ii), we get, $A=8N;B=2N$
When each force is increased by 3N, then
$A^{\prime }=A+3=8+3=11N,B^{\prime }=B+3=2+3=5N$.
As the new forces are acting at an angle of ${90}^{\circ }(i.e.,\theta ={90}^{\circ })$
so $R^{\prime }=\sqrt{A^{\prime 2}+B^{\prime 2}}=\sqrt{(11{)}^2+(5{)}^2}=\sqrt{146}N.$