Question

# A particles performing uniform circular motion. Its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A
L4
B
2L
C
4L
D
L2

Solution

## The correct option is B $$\displaystyle\frac{L}{4}$$$$\mbox{Angular momentum} \propto \displaystyle\frac{1}{\mbox{Angular frequency}} \propto \mbox{Kinetic Energy}$$$$\Rightarrow \bar{L} = \displaystyle\frac{K.E.}{\omega}$$$$\displaystyle\frac{L_1}{L_2} = \left(\displaystyle\frac{K.E_1}{\omega_1}\right)\times\displaystyle\frac{\omega_2}{K.E_2} = 4 \Rightarrow L_2 = \displaystyle\frac{L}{4}$$Physics

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