Question

For increasing the angular velocity of a object by $10$%, the kinetic energy has to be increased by

• A. $40$%
• B. $20$%
• C. $10$%
• D. $21$%

Answer 1

The correct option is D $21$%

Let initial energy be $K$ and angular velocity be $w$ after change become $K^{\prime }$and$w^{\prime }$

${\omega }^{\prime }=1.1\omega \left(given\right)K=\frac{1}{2}I{\omega }^2{K}^{\prime }=\frac{1}{2}I({\omega }^{\prime }{)}^2=\frac{1}{2}I(1.1\omega {)}^2=1.21\left(\frac{1}{2}I{\omega }^2\right)=1.21K$

Therefore kinetic energy should be increased by 21%