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

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

System of Particles and Rotational Motion

Solution:

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