Question

A uniform rod of mass $M$ has an impulse applied at right angles to one end. If the other end begins to move with speed $V$, the magnitude of the impulse is

• A. $2MV/3$
• B. $MV$
• C. $MV/2$
• D. $2MV$

Answer 1

The correct option is C $MV/2$


From the free body diagram, the impulse is given by

$J=M{V}_{COM}$

$\Rightarrow V_{COM}=\frac{J}{M}$

Taking moment of $\text{J}$ about $\text{COM}$

$J\frac{L}{2}=\text{I}\omega =\frac{M{L}^2}{12}\omega$

$\Rightarrow \omega =\frac{6J}{ML}$

So from figure, $V=|\frac{J}{M}-\frac{6J}{ML}\frac{L}{2}|$

$\therefore J=\frac{MV}{2}$

Thus, the correct option is $\text{(B)}$.