A rod of mass , length is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end of the rod with a velocity in a direction perpendicular to The collision is completely elastic. After the collision ,the Particle comes to rest. The ratio Is


a) 
b) 
c) 

d) 
A rod of mass , length is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end of the rod with a velocity in a direction perpendicular to The collision is completely elastic. After the collision ,the Particle comes to rest. The ratio Is


a) 
b) 
c) 

d) 
(a)
Since, linear momentum is conserved
Angular momentum is also conserved
Where is the moment of inertia of the rod about the axis of rotation
Since, collision is completely elastic , kinetic energy is also conserved .Thus,
From Eqs. (i)and (ii),We get
Putting this value in Eq. (iii),we get
OR