Answer:
Initial angular momentum of one disc. \[L=I\omega
=\frac{1}{2}M{{R}^{2}}\omega \]
When another disc. of mass\[\frac{M}{4}\]
and radius R is placed gently on it, total moment of inertia of the combination
is \[I'=\frac{1}{2}M{{R}^{2}}+\frac{1}{2}\left( \frac{M}{4}
\right){{R}^{2}}=\frac{5}{8}M{{R}^{2}}\]
As no external torque has been
applied, angular momentum is conserved.
\[\therefore \] \[I'\omega '=I\omega ,\] \[\omega
'=\frac{I\omega }{I'}\frac{\frac{1}{2}M{{R}^{2}}\omega
}{\frac{5}{8}M{{R}^{2}}}=\frac{4}{5}\omega \]
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