A particle of mass m strikes elastically with a disc of radius R, with a velocity v as shown in the Fig. If the mass of the disc is equal to that of the particle and the surface of contact is smooth, find the velocity of the disc just after the collision.

A particle of mass m strikes elastically with a disc of radius R, with

1.	A particle of mass m strikes elastically with a disc of radius R, with a velocity v as shown in the Fig. If the mass of the disc is equal to that of the particle and the surface of contact is smooth, find the velocity of the disc just after the collision.
Answer» Solution :Impact takes PLACE along the line of impact, which is normal at the point of impact. Hence, the momentum of particle and the disc changes along line of impact. However, no external force acts on the system along the normal line. Hence we can conserve the LINEAR momentum of the system (disc + particle) along the normal. Since the MASSES of the disc and particle are equal, the particle completely DELIVERS component of its momentum `(mvcostheta)` along the normal. Velocity of the disc = `v _(1) = (v cos theta ) j` since `theta = (R//2)/(R ) = (1)/(2) cos theta = sqrt (1- ((1)/(2)) ^(2)) = (sqrt3)/(2) ,v _(1) = (sqrt3v)/( 2) hatj` Finaly the particle possess the velocity `v sin theta ` along x- axis and disc possesses the velocity `v cos theta` along y-axis.