When a body is hinged at a point and a force is acting on the body in such a way that the line of action of force is at some distance from the hinged point, the body will start rotating about the hinged point. The angular acceleration of the body can be calculated by finding the torque of that force about the hinged point. A disc of mass `m` and radius `R` is hinged at point `A` at its bottom and is free to rotate in the vertical plane. A force of magnitude `F` is acting on the ring at top most point.

Component of reaction at the hinge in the horizontal direction is

Options

A. `F/4`
B. `F`
C. `F/3`
D. `F/2`

Answer

C

Explanation

Torque about the `CM`
`(F-R_(x))R=Ialpha`
`implies(F-R_(x))R=(Mr^(2)a_(t))/(2 r)`
`implies (F-R_(x))R=(2F)/3`
`implies F=(2F)/3=R_(x)impliesR_(x)=F/3`