Question

A block of mass ? slides along a frictionless surface with a speed ? and collides with a stationary block of mass 2? . After the collision the block of mass ? rebounds with a speed of ?⁄2. What is the greatest speed ???? that the block of mass 2? can have after the collision?

Answer 1

Here,it occurs the elastic collition between the two masses of mass 'm' moving at a velocity towards another mass '2m' which is at rest in the line of same path of mass 'm'.

So the body of mass 'm' collides the larger body of mass '2m' which are sliding through a surface offering no frictional resistance or any other loss of energy(since,it is elastic collision)

As a result of the collision between between the masses,the smaller mass is rebounded back its direction with velocity of 'v/2' and let the velocity of the larger mass after collision be (v').As shown in the figure given below.

As per the theory of conservation of momentum in this collission,

Sum of the momentum of the bodies before collission =sum of momentum of bodies after collission

sum of momentum of bodies before collission,

( V"=0,as larger mass is at rest initially)

after collission, velocity of mass 'm'=-v/2  (since it is rebounds back)

let velocity of mass 2m,=V'

so,sum of momentum of bodies after collission=

ie,

So it is found that the velocity of larger mass '2m' is moving in the same direction (+x axis) with a velocity of

so it is the maximum velocity got by the larger mass,