A solid disk of mass M and radius R is free to rotate about the axis as shown in the figure. The inner hub is massless but has radius r.  Around this inner hub is wrapped a string as shown that goes over a frictionless pulley and is attached to a hanging mass m. The mass m is acted upon by gravity. The normal
force of the table cancel the weight of the disk.  The disk starts at rest
and, thereafter, the string slowly unwinds without sliping on the pulley or the
hub.

What is the expression that relates the liner acceleration of the string to the
tension in the string and the small mass?

a=(T+mg)/m
a=g
a=(T-mg)/m
insufficient information

What is the expression that relates the angular acceleration of the disk
to the tension in the string

\alpha=\frac{2rT}{MR^2}

\alpha=\frac{MR^2}{2rT}

\alpha=\sqrt{\frac{MR^2}{2rT}}

\alpha= 2rTMR^2


Given that M=1 kg, R = 0.20 m (for the disk), r= 0.02 m (for the hub) and m=0.1 kg (for the hanging mass), what is the approximate error introduced into the value of alpha if the $mr^2$ term in the expression I+mr^2 is neglected.

a 0.2%
b 1%
c 5%
d 20%