A body of moment of inertia of 3 kg-m² rotating with an angular velocity of 2 rad/sec has the same kinetic energy as a mass of 12 kg moving with a velocity of

The correct answer/option is 1 m/s.

To find the velocity of the moving mass, we equate the rotational kinetic energy of the rotating body to the translational kinetic energy of the moving mass.

Step 1: Calculate the rotational kinetic energy of the rotating body.
The formula for the rotational kinetic energy ($E_r$) is:
$E_r=\frac{1}{2}I{\omega }^2$
Given:
Moment of inertia, $I=3\text{kg·m}{²}^{}$
Angular velocity, $\omega =2\text{rad/s}$
Substituting these values:
$E_r=\frac{1}{2}\times 3\times (2{)}^2$
$E_r=\frac{1}{2}\times 3\times 4=6\text{J}$

Step 2: Relate to the translational kinetic energy of the mass.
The formula for translational kinetic energy ($E_t$) of a moving mass is:
$E_t=\frac{1}{2}m{v}^2$
Given:
Mass, $m=12\text{kg}$
Since the kinetic energy is the same:
$E_t=E_r=6\text{J}$

Step 3: Solve for the velocity ($v$).
Substitute the values into the translational kinetic energy equation:
$6=\frac{1}{2}\times 12\times v^2$
$6=6v^2$
$v^2=1$
$v=1\text{m/s}$

Therefore, the velocity of the mass is 1 m/s.