Question

At time T, when the side $BC$ is parallel to the x-axis, a force F is applied on B along $BC$ (as shown).Obtain the x-component and the y-component of the force exerted by the hinge on the body,immediately after time $T$.

Answer 1

Angular acceleration of system about point A is
$\alpha =\frac{\tau T_A}{I_A}$
$=\frac{\left(F\right)\left(\frac{\sqrt{3}}{2}l\right)}{2m{l}^2}$
$=\frac{\sqrt{3}F}{4ml}$
Now) acceleration of $COM$ along x-axis is
$a_x=r\alpha =\left(\frac{l}{\sqrt{3}}\right)\left(\frac{\sqrt{3}F}{4ml}\right)$ or $a_x=\frac{F}{4m}$
Now, let $F$, be the force applied by the hinge along x-axis
Then, $F_x+F=\left(3m\right)a_x$
or $F_x+F=\left(3m\right)\left(\frac{F}{4m}\right)$
or $F_x+F=\frac{3}{4}F$ or $F_x=-\frac{F}{4}$
Furtner if $F_y$ be the force applied by the hinge along y-axis. Then,
$F_y=$ centripetal force
$F_y=\sqrt{3}m{\omega }^2$