A uniform rod of mass `M_(1)` is hinged at its upper end as shown in the figure . A particle of mass `M_(2)` which is moving horizontally, strikes the rod elastically at its midpoint. If the particle comes to rest after collision then the value of `(M_1)/(M_2)` is

Answer

`0.75`

Explanation

Conserving angular momentum about the hinge, just before and after the collision
`L_(H)=M_(2)v L/2=(M_(1)L^(2))/3omega`
There fore `omega=(3M_(2)v)/(2M_(1)L)`
Also
`e=1,V_(CM)=v=(omegaL)/2`
`implies(2v)/L=(3M_(2)v)/(2M_(1)L)`
`implies(M_(1))/(M_(2))=3/4`
`=0.75`