Question

A uniform rod of mass $m=0.5kg$ and length $90$ cm rests on a smooth horizontal surface. One of the ends of the rod is stuck with impulse $J=3.0Ns$ in a horizontal direction perpendicular to the rod as shown in fig. As a result the rod obtains momentum $p=3.0Ns$. Find

Answer 1

Find velocity of centre of mass and angular velocity.

$\Rightarrow J\left(\frac{l}{2}\right)=\frac{m{l}^2}{12}.w$

$\Rightarrow 3\times \frac{45}{100}=\frac{0.5}{12}\left(0.9\times 0.9\right)w$

$\Rightarrow w=4rad/\sec$

Now,

$\Rightarrow J=mV$

$\Rightarrow V=\frac{J}{m}=\frac{3}{0.5}=6m/s$

Hence,

we get,

$V=6m/s$