NEET Physics Rotational Motion NEET PYQ-Rotational Motion

Two bodies have their moments of inertia \[l\] and \[2l\] respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:           [AIPMT (S) 2005]

A) 1 : 2

B) \[\sqrt{2}\,:1\]

C) 2 : 1

D) \[1:\sqrt{2}\]

Correct Answer: D

Solution :

As said, \[{{(KE)}_{\text{rot}}}\] remains same.

i.e., \[\frac{1}{2}{{I}_{1}}\omega _{1}^{2}=\frac{1}{2}{{I}_{2}}\omega _{2}^{2}\]

\[\Rightarrow \] \[\frac{1}{2{{I}_{1}}}{{({{I}_{1}}{{\omega }_{1}})}^{2}}=\frac{1}{2{{I}_{2}}}{{({{I}_{2}}{{\omega }_{2}})}^{2}}\]

\[\Rightarrow \] \[\frac{L_{1}^{2}}{{{I}_{1}}}=\frac{L_{2}^{2}}{{{I}_{2}}}\]

\[\Rightarrow \] \[\frac{{{L}_{1}}}{{{L}_{2}}}=\sqrt{\frac{{{I}_{1}}}{{{I}_{2}}}}\]

but \[{{I}_{1}}=I,\,\,{{I}_{2}}=2I\]

\[\therefore \] \[\frac{{{L}_{1}}}{{{L}_{2}}}=\sqrt{\frac{I}{2I}}=\frac{1}{\sqrt{2}}\]

or \[{{L}_{1}}:{{L}_{2}}=1:\sqrt{2}\]