Question

A particle is undergoing uniform circular motion with angular momentum $L$. While moving on the same path if its kinetic energy becomes four times, then its angular momentum will be

• A. L/4
• B. L/2
• C. L
• D. 2L

Answer 1

Answer: (D)

Angular momentum during uniform circular motion $L=mvr$
Kinetic energy $K=\frac{1}{2}m{v}^2$
$=\frac{1}{2}m\times {\left(\frac{L}{mr}\right)}^2=\frac{L^2}{2m{r}^2}$
According to the question,
$K^{\prime }=\frac{{\left(L^{\prime }\right)}^2}{2m{r}^2}=4K$
$\Rightarrow \frac{{\left(L^{\prime }\right)}^2}{2m{r}^2}=\frac{4\times L^2}{2m{r}^2}$
$\Rightarrow L^{\prime }=2L$