Question

A body of moment of inertia of $3kg-m^2$ is rotating with an angular velocity of 2 rad/sec and has the same kinetic energy as a mass of 12 kg moving with a velocity of

• A. 8 m/s
• B. 0.5 m/s
• C. 2 m/s
• D. 1 m/s

Answer 1

The correct option is D 1 m/s

Rotational kinetic energy of the body $=\frac{1}{2}I{\omega }^2$ and translatory kinetic energy $=\frac{1}{2}m{v}^2$
According to problem $=\frac{1}{2}I{\omega }^2=\frac{1}{2}m{v}^2\Rightarrow \frac{1}{2}\times 3\times (2{)}^2=\frac{1}{2}\times 12\times v^2\Rightarrow v=1m/s.$