question_answer

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

Correct Answer: D

Solution :

 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, \[K=\frac{{{(L)}^{2}}}{2m{{r}^{2}}}=4K\] \[\Rightarrow \] \[\frac{{{(L)}^{2}}}{2m{{r}^{2}}}=\frac{4\times {{L}^{2}}}{2m{{r}^{2}}}\] \[\Rightarrow \] \[L=2L\]