Question

A string is wrapped on a wheel of moment of inertia 0.20 $kg-m^2$ and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure (10-E5). Find the acceleration of the block.

Answer 1

I = 0.20 $m^2\text{Bigger pulley}$ r = 10 $\text{cm}=0.1m,\text{Smaller pulley is light}$ $\text{Mass of the block},m=2kg$ $\text{Therefore,}mg-T=ma...\left(1\right)$ $\text{T}\times \text{r}=\text{I}\times \alpha$ $\Rightarrow \text{T}=\frac{Ia}{r^2}...\left(2\right)$ $\Rightarrow mg=(m+\frac{I}{r^2})a$ $\left[\text{Using}\right(2\left)\text{in}\right(1\left)\right]$ $\Rightarrow a=\frac{mg}{(m+\frac{I}{r^2})}$ $=\frac{2\times 9.8}{\{2+\left(\frac{0.2}{0.01}\right)\}}$ $=\frac{19.6}{22}=0.89m/s^2$