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
mg3
B
2mg3
C
mg2
D
mg

Solution

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

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