Question

A uniform rod AB of length 1.2 m is at rest on a smooth horizontal surface. if an impulse is applied at a distance x from end A, perpendicular to rod in horizontal direction, so that end A does not move just after the impulse. Find x (in cm)

Answer 1

For A not to move

$V_{cm}=\frac{\omega \ell }{2}$

$J=m{v}_{cm}$

$Jy=\frac{m{\ell }^2}{12}\omega$

$\Rightarrow y=\frac{m{\ell }^2\omega }{12J}=\frac{\ell }{6}$

$\Rightarrow x=\frac{\ell }{2}+\frac{\ell }{2}=\frac{2\ell }{3}=0.8m=80cm$