A rod AB of mass M and length 4L rests on a smooth horizontal plane. A small particle P moving with a velocity V strikes the rod elastically in a direction normal to the length, at a point distant L from the centre C of the rod. Immediately after the collision, if P comes to rest, then its mass should be
Let m be the mass of that particle from conservation of linear momentum, mv=0+MVc where Vc is
linear velocity of cm of the rod.
From conservation of angular momentum, mVL=Iω
As collision is elastic,
V=Vc+wL⇒V=mVM+mVL2I⇒(mM+mL2I)=1But I=M(4L)212Then mM(1+34)=1⇒m=4M7