Question

A uniform rod of mass 2 kg and length 3 m is moving such that velocity of its one end is 4m/s towards right while the angular velocity of the rod is 2 rad/s, in clockwise direction as shown.The kinetic energy (in Joule) of the rod is:

• A. 4
• B. 2
• C. 1
• D. 6

Answer 1

The correct option is A 4

We have the linear velocity of the topmost point as $4m/s$ and it is given that the angular velocity of the rod is $2rad/s$ about some point.
Let us find this point first
$v=x\omega$ or $4=x\times 2$
or
$x=2$
Thus, we get the kinetic energy as $\frac{1}{2}I{\omega }^2$(about the center of rotation).
Note that the center of rotation does not have any translational velocity
or
$\frac{1}{2}(\frac{m{l}^2}{12}+m({0.5}^2\left)\right)2^2$
or
$KE=4J$