MCQ
A body of moment of inertia of $3\ kg-m^2$ 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 .......... $m/s$
- A$8$
- B$0.5$
- C$2$
- ✓$1$
✓
Answer
Correct option: D.
$1$
d
Rotational kinetic energy of the body = $\frac{1}{2}I{\omega ^2}$ and translatory kinetic energy $ = \frac{1}{2}m{v^2}$
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}$ Þ $\frac{1}{2} \times 3 \times {(2)^2}$
$= \frac{1}{2} \times 12 \times {v^2}$ $⇒$ $v = 1\,m/s$.
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