Discus the folwing as special cases of elastic collision and obtain their exact or approximate final velocities in terms of their initial velocities.

Two bodies of masses m and 2m, moving with initial velocities 50 m//s in the + x direction and 40 m//s in the -x direction respectively, undergo a head -on elastic collision. (i) Calculate their final velocities (ii) What is the ratio of the final to initial kinetic energies for the body of mass m? (iii) Calculate the change in momentum of each body if m= 1kg (iv) What is the change in the momentum of the system?

A sphere of mass 'm' moving with velocity 'v' collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)

Define in elastic collision. Derive an expression for velocities for head-on elastic collision.

State the expression of final velocity of 2 bodies having a head on elastic collision.

Two particles of masses m_(1),m_(2) move with initial velocities u_(1) and u_(2) . On collision, one of the particles get excited to higher level, after absording enegry. If final velocities of particles be v_(1) and v_(2) then we must have

v = at + frac(b)(t+c) + v_0 is dimensionally valid equation Obtain the dimensional formula for a,b,c where v is velocity, t is time and vunderset(0) is initial velocity.

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

Derive expression for final velocities v_1 and v_2 for an Elastic collsion.

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :