Question

If angular momentum of a body is increased by $200$% its kinetic energy will increase by

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

Answer 1

The correct option is B $800$%

Kinetic energy $K=\frac{L^2}{2I}$
where $L$ is the angular momentum of a body $I$ is the moment of inertia of a body.
When the angular momentum of a body is increased by $200$%, its new momentum $L^{\prime }$ will become
$L^{\prime }=L+\frac{200L}{100}=3L$
$\frac{K^{\prime }}{K}={\left(\frac{L^{\prime }}{L}\right)}^2={\left(\frac{3L}{L}\right)}^2=9$
$\therefore K^{\prime }=9K$
% increase in kinetic energy $=\frac{K^{\prime }-K}{K}\times 100$
$=\frac{9K-K}{K}\times 100=800$%.