Q. 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:
The center of mass (the same with the center of weight) of a right triangle is 1/3 distance from the right angle on both legs.
The momentum of the triangle weight plus that of the force in B with respect to point A is zero (the plate does not rotate about A)
`G*(l/3) -F_B*l =0`
`F_B =G/3` directed upwards.
Now for static equilibrium one needs that on the vertical axis the sum of all forces is zero.
`F_A + F_B -G = 0`
`F_A =G-F_B =G-G/3 =(2/3)*G =(2/3)*m*g`
The correct answer is B) `(2*mg)/3`