A string is wrapped around a cylinder of mass M and radius R. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string. The tension in the string is

Equation of motion is

$Mg-T=Ma..........\left(ii\right)$

Taking torque about the axis passing through the centre of the spool and perpendicular to it,

$\begin{array}{l}TR=I\alpha =\frac{1}{2}M{R}^2\left(\frac{a}{2}\right)\\ T=\frac{1}{2}Ma............\left(ii\right)\end{array}$

From Eqs. (i) and (ii),

$\begin{array}{l}Ma=Mg-\frac{1}{2}Ma\\ a=\frac{2g}{3}\\ \therefore T=\frac{Mg}{3}\end{array}$