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  4. A uniform disc of mass M and radius R is mounted on a fixed horizontal axis. A block of mass m hangs from a massless string that is wrapped around the rim of the disc. The magnitude of the acceleration of the falling block ( m ) is

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Q. A uniform disc of mass $M$ and radius $R \, $ is mounted on a fixed horizontal axis. A block of mass $m$ hangs from a massless string that is wrapped around the rim of the disc. The magnitude of the acceleration of the falling block ( $m$ ) is

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

When pulley has a finite mass $M$ and radius $R$ , then tension in two segments of the string are different.

Solution
Here, $ma=mg-T$
$a=\frac{m}{m + \frac{M}{2}}g=\frac{2 m}{2 m + M}g$