Question

Four forces, tangent to the radius $R$, are acting on a wheel as shown in the figure. The resultant equivalent one force system will be,

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

For the equivalent force system, $F_{net}$ & ${\tau }_{net}$, about point $O$ must be same.

$F_{net}:$

$\Rightarrow$ $F_{net}=\sqrt{(400{)}^2+(300{)}^2}=500\text{N}$
and, $\tan \alpha =\frac{400}{300}\Rightarrow \alpha ={53}^{\circ }$

& about point $O$,
${\tau }_{net}=400R-200R+200R+100R$
$=500R\text{(Clockwise)}$
So, the system can be shown as


Hence, $\left(C\right)$ is the correct answer.