Question

A body having a moment of inertia about its axis of rotation equal to 3 $kg-m^2$ is rotating with angular velocity of $3rad{s}^{-1}$. Kinetic energy of this rotating body is same as that of a body of mass $27kg$ moving with velocity $v$. The value of $v$ is

• A. 1 $s^{-1}$
• B. 0.5 $s^{-1}$
• C. 2 $s^{-1}$
• D. 1.5 $s^{-1}$

Answer 1

The correct option is A 1 $s^{-1}$

Given : $I=3$ $kg.m^2$ $w=3$ $rad/s$ $m=27$ kg

Rotational kinetic energy of the body is same as the translational kinetic energy of body of mass $27$ kg

$\therefore$ $\frac{1}{2}I{w}^2=\frac{1}{2}m{v}^2$

Or $\frac{1}{2}\times 3\times 3^2=\frac{1}{2}\times 27v^2$ $⟹v=1$ $m/s$