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6.System of Particles and Rotational Motion
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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
$2$
D
$1$
Solution
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 $\frac{1}{2} \times 3 \times {(2)^2}$
$= \frac{1}{2} \times 12 \times {v^2}$ $⇒$ $v = 1\,m/s$.
Standard 11
Physics
