A right triangular plate ABC of mass m is free to rotate in vertical plane about a fixed horizontal

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6.System of Particles and Rotational Motion

hard

$A$ 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

$mg$

Solution

The distance of Centre Of Mass of given right angled triangle is $\frac{2 L}{3}$ along $\mathrm{BA}$ and $\frac{L}{3}$

along $AC$ from the point $B.$

Force of magnitude $m g$ is acting downwards at its COM.

Moment balance around $B$ gives$:$

$m g\left(\frac{2 L}{3}\right)-F_{A}(L)=0$

(Momente $\left.\vec{r} \times \vec{F}=r F \sin (\theta)=F(r \sin (\theta))=F r_{\perp}\right)$

$\therefore F_{A}=\frac{2}{3} m g$

Standard 11

Physics

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