Question

If the angular momentum of a rotating body is increased by $200\%,$ then its kinetic energy of rotation will be increased by

• A. $400\%$
• B. $800\%$
• C. $200\%$
• D. $100\%$

Answer 1

The correct option is B $800\%$

As $E=\frac{L^2}{2I}\Rightarrow \frac{E_2}{E_1}={\left(\frac{L_2}{L_1}\right)}^2={\left(\frac{3L_1}{L_1}\right)}^2$ $[As{L}_2=L_1+200\%.L_1=3L_1]$
$\Rightarrow E_2=9E_1=E_1+800\%of{E}_1$