Question

A fixed pulley of radius $10cm$ and moment of inertia $0.01kg$ $m^2$ about its axle has a massless cord wrapped around its rim. A $1kg$ mass is attached to the end of the cord. The pulley can rotate about its axis without any friction. Find the acceleration of the mass : (Assume $g=10m/s^2$)

Answer 1

$\begin{array}{c}\overline{\tau }=\frac{d\overline{i}}{dt}\\ mgr=\frac{d}{dt}\left[mvr+I.\frac{v}{R}\right]\\ mg=\left(M+\frac{I}{R^2}\right)a\\ a=\frac{mg}{M+\frac{I}{R^2}}\\ =\frac{1\times 10}{7+\frac{0.01}{0.01}}\\ =5m/s^2\end{array}$