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