Q. A body having moment of inertia about its axis of rotation equal to $3\ kg - m^{2}$ is rotating with angular velocity equal to $3\ rad/s$. Kinetic energy of this rotating body is the same as that of body of mass $27\ kg$ moving with a speed of
A) $1.0\ m/s$
B) $0.5\ m/s$
C) $1.5\ m/s$
D) $2.0\ m/s$
Explanation
(a) Kinetic energy of rotating body $= \frac{1}{2}I\omega^{2}$
$= \frac{1}{2} \times 3 \times (3)^{2} = 13.5\ J$
Kinetic energy of translating body $= \frac{1}{2}mv^{2}$
As both are equal according to problem $i.e.$
$\frac{1}{2}mv^{2} = 13.5 \Rightarrow \frac{1}{2} \times 27 \times v^{2} = 13.5 \Rightarrow \ \therefore v = 1m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.