A) \[\frac{L}{2}\]
B) \[2L\]
C) \[4L\]
D) \[\frac{L}{4}\]
Correct Answer: D
Solution :
The angular momentum is measure for the amount of torque that has been applied over time to the object. For a particle with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as \[L=I\omega \] ....(i) where I is moment of inertia of particle and\[\omega \]the angular velocity. Also, \[K=\frac{1}{2}I{{\omega }^{2}}\] ...(ii) where K is kinetic energy of rotation. From Eqs. (i) and (ii), we get \[L=\frac{2K}{{{\omega }^{2}}}\omega =\frac{2K}{\omega }\] \[L=\frac{2(K/2)}{2\omega }=\frac{1}{4}\left( \frac{2K}{\omega } \right)=\frac{L}{4}\] Note: In a closed system angular momentum is constant.
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