Question

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

• A. $\frac{L}{4}$
• B. $2L$
• C. $4L$
• D. $\frac{L}{2}$

Answer 1

Answer: (A)

$\frac{L}{4}$

$\text{Angular momentum}\propto \frac{1}{\text{Angular frequency}}\propto \text{Kinetic Energy}$
$\Rightarrow \overline{L}=\frac{K.E.}{\omega }$
$\frac{L_1}{L_2}=\left(\frac{K.E_1}{{\omega }_1}\right)\times \frac{{\omega }_2}{K.E_2}=4\Rightarrow L_2=\frac{L}{4}$