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

Answer 1

Answer:

$\frac{2mg}{3}$

Step-by-step explanation:

The center of mass 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.

$G(\frac{1}{3} ) - F_{B} * l = 0$

$F_{B} = \frac{G}{3}$ directed upwards

Now for static equilibrium one needs that on the vertical axis the sum of all forces is zero.

$F_{S} + F_{B} - G = 0$

$F_{A} = G - F_{B} = G - \frac{G}{3} = \frac{2}{3} G = \frac{2mg}{3}$

Hence, the answer is $\frac{2mg}{3}$