Question

Figure shows a uniform disk, with mass $M=2.4kg$ and radius $R=20cm$, mounted on a fixed horizontal axle. A block of mass $m=1.2kg$ hangs from a massless cord that is wrapped around the rim of the disk. The tension (in newton) in cord is

Answer 1

Answer: 6

For block: $mg-T=ma...(i)$
For disk (pulley) $TR=I\alpha =\frac{M{R}^2}{2}\alpha$
But $\alpha =\frac{a}{R}$ so $T=\frac{Ma}{2}...(ii)$
Therefore
$\frac{mg-T}{T}=\frac{2m}{M}$
$\Rightarrow \frac{mg}{T}=\frac{2m}{M}+1$
$\Rightarrow T=\frac{mg}{\left(\frac{2m}{M}+1\right)}=\frac{(1.2\times 10)}{\left(\frac{211.2}{2.4}+1\right)}=6N$