A uniform rod of length L lies on a smooth horizontal table. A particle moving on the table strikes the rod perpendicularly at an end and stops. Find the distance travelled by the centre of the rod by the time it turns through a right angle. Show that if the mass of the rod is four times that of the particle, the collision is elastic

Answer

A, B

Explanation

Let the mass of the particle =m
and the mass of the rod =M
Let the particles stirke the rod with as velocity V.
If we take two body to be a system.
Therefore the net externla torque and exterN/Al force =0


Therfore applying laws of conservation of linear momentum
`MV'=mV`
`(V'=velocity of the rod after striking)
`rarrV'/V=m/M`
Again applying laws of conservatioin of angular momentum
`rarr (mVR)/2=I omega`
`-(mVR)/2=((MR^2)/12)xx(pi/(2t))`
`t=((MRpi)/(mxx12xxV))`

`Therefore distance travelled
`=Vt=V'(Mrpi)(m12pi)`
`=(m/M)xx(M/m)xx((RPi)/12)`
`=(Rpi)/12`