Question

The maximum resultant of two forces is $2P$ and the minimum resultant is $2Q$, the two forces are at right angles, then the resultant is

• A. $P+Q$
• B. $P-Q$
• C. $\sqrt{\frac{P^2+Q^2}{2}}$
• D. $\sqrt{2(P^2+Q^2)}$

Answer 1

The correct option is D $\sqrt{2(P^2+Q^2)}$

Let the two forces be $F_1$ and $F_2$.
Then, maximum resultant $=2P=F_1+F_2$
and minimum resultant $=2Q=F_1-F_2$
Thus, $F_1=P+Q$ and $F_2=P-Q$
$\therefore$ Resultant $\left(R\right)=\sqrt{F_1^2+F_2^2}$
$=\sqrt{2P^2+2Q^2}=\sqrt{2(P^2+Q^2)}$