Option B $-$ Engineering physics

$11.$ A flywheel consists of a solid cylinder, with a small radial axle protruding from its centre.

The following data are available for the flywheel.

Flywheel mass $M=1\mathrm{.}22kg$

Small axle radius $r=60\mathrm{.}0mm$

Flywheel radius $R=240mm$

Moment of inertia $=0\mathrm{.}5M{R}^2$

An object of mass $m$ is connected to the axle by a light string and allowed to fall vertically from rest, exerting a torque on the flywheel.

$($a$)$ The velocity of the falling object is $1\mathrm{.}89m{s}^{-1}$ at $3\mathrm{.}98s.$ Calculate the

$[2]$

average angular acceleration of the flywheel.

$6$

$($b$)$ Show that the torque acting on the flywheel is about $0\mathrm{.}3Nm.$