Question

The magnitude of the two forces forming a couple is $ 36\, N $ each and the arm of the couple is $ 4 \,m $ . The magnitude of each force of an equivalent couple whose arm is $ 9\, m $ , is (in Newtons)

• A. 18
• B. 26
• C. 16
• D. 15

Answer 1

Answer: (C)

Moment of couple $= \vec{F} \times \vec{ A B }$
where $F$ is force and $A B$ is distance.
Since, $F_{1}=36 N , d_{1}=4 m , F_{2}=F($ say $)$
and $d_{2}=9 m$
Also, $ F_{1} \times d_{1}=F_{2} \times d_{2}$
$\Rightarrow 36 \times 4=F \times 9$
$\Rightarrow =16 N$