Question

At shown instant a thin uniform rod AB of length $L$ $=$ $1$m and mass $m$ $=$ $1$ kg is coincident with y-axis such that centre of rod is at origin. The velocity of end A and centre O of rod at shown instant are $\overrightarrow{V_A}=-2\hat{i}m/s$ and $\overrightarrow{V_0}=10\hat{i}m/s$respectively. Then the kinetic energy of rod at the shown instant is :

• A. $42J$
• B. $56J$
• C. $74J$
• D. None of these

Answer 1

Answer: (C)

$74J$

Moment of Inertia of a rod = $\frac{M{L}^2}{12}$
The kinetic energy is given as $\frac{1}{2}m{v}_{cm}^2+\frac{1}{2}{I}_{cm}{\omega }^2$
or
$\frac{1}{2}1\left({10}^2\right)+\frac{1}{2}\frac{\left(1\right)(1{)}^2}{12}\frac{{12}^2}{{0.5}^2}=74J$