Question

A right triangular plate ABC of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is :

• A. $\frac{mg}{3}$
• B. $\frac{2mg}{3}$
• C. $\frac{mg}{2}$
• D. $mg$

Answer 1

Answer: (B)

$\frac{2mg}{3}$

The distance of Centre Of Mass of given right angled triangle is $\frac{2L}{3}$ along BA and $\frac{L}{3}$ along AC from the point B.
Force of magnitude $mg$ is acting downwards at its COM.
Moment balance around B gives:
$mg\left(\frac{2L}{3}\right)-F_A\left(L\right)=0$
(Moment= $\overrightarrow{r}\times \overrightarrow{F}=rFsin\left(\theta \right)=F\left(rsin\right(\theta \left)\right)=F{r}_{\perp }$)
$\therefore F_A=\frac{2}{3}mg$