Collision is an isolated event in which a strong force acts between two or more bodies for a short time as a result of which the energy and momentum of the interacting particle change.
In collision particles may or may not come in real touch e.g. in collision between two billiard balls or a ball and bat there is physical contact while in collision of alpha particle by a nucleus (i.e. Rutherford scattering experiment) there is no physical contact.
Collision is of two types- On the basis of conservation of kinetic energy
Both momentum and kinetic energy remains conserved.
Only momentum remains conserved. There is loss in kinetic energy.
Coefficient of restitution: (e)
The ratio of relative velocity of separation and relative velocity of approach is defined as
coefficient of restitution.
For perfectly elastic collision, e=1
For perfectly inelastic collision, e=0
For inelastic collision, 0<e<1
In short we can say that ‘e’ is the degree of elasticity of collision and it is dimension less quantity.
On the basis of the direction of colliding bodies– collision is of two types.
Head on or one dimensional collision:
In a collision if the motion of colliding particles before and after the collision is along the same line the collision is said to be head on or one dimensional.
If two particle collision is ‘glancing’ i.e. such that their directions of motion after collision are not along the initial line of motion, the collision is called oblique.
If in oblique collision the particles before and after collision are in same plane, the collision is called 2- dimensional otherwise 3-dimensional.
Q.1. Which one of the following statements is true?
(a) Momentum is conserved in elastic collisions but not in inelastic collisions
(b) Total kinetic energy is conserved in elastic collisions but momentum is not conserved in elastic collisions
(c) Total kinetic energy is not conserved but momentum is conserved in inelastic collisions
(d) Kinetic energy and momentum both are conserved in all types of collisions
Answer(c) The law of conservation of momentum is true in all type of collisions, but kinetic energy is conserved only in elastic collision. The kinetic energy is not conserved in inelastic collision but the total energy is conserved in all type of collisions.
Q.2. When after collision the deformation is not relived and the two bodies move together after the collision, it is called
(a) elastic collision
(b) inelastic collision
(c) perfectly inelastic collision
(d) perfectly elastic collision
Answer(c) In a perfectly inelastic collision, the two bodies move together as one body.
Q.3. In an inelastic collision, which of the following does not remain conserved?
(b) kinetic energy
(c) Total energy
(d) Neither momentum nor kinetic energy
Answer(b) In an inelastic collision, momentum remains conserved, but K.E is changed.
Q.4. The coefficient of restitution e for a perfectly elastic collision is
Q.5. The coefficient of restitution e for a perfectly inelastic collision is
Q.6. When two bodies stick together after collision, the collision is said to be
(a) partially elastic
(d) perfectly inelastic
Q.7. In elastic collision, 100% energy transfer takes place when
(a) m1 = m2
(b) m1 > m2
(c) m1 < m2
(d) m1 = 2m2
Answer(a) During elastic collision between two equal masses, the velocities get exchanged. Hence energy transfer is maximum when m1 = m2.
Q.8. When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after collision they will move
(a) opposite to one another
(b) in the same direction
(d) at right angle to each other
Answer(d) When two spheres of equal masses undergo a glancing elastic collision with one of them at rest, after the collision they will move at right angle to each other.
Q.9. The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact
(a) is extremely small
(b) is moderately small
(c) is extremely large
(d) depends on particular case
Answer(a) In physics, collision does not means that are particle strike another particle. Infact, two particles may not even touch each other & may still said to be colliding.
The necessary requirements of collision are
(i) A large force for a relatively short time (i.e., an impulse) acts on each colliding particle.
(ii) The motion of the particles (at least one of the particle) is changed abruptly.
(iii) The total momentum (as also the total energy) of particles remains conserved.
Q.10. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
Q.11. A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be
(a) 0, 1
(b) 1, 1
(c) 1, 0.5
(d) 0, 2
Q.12. A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is
(a) 140 J
(b) 100 J
(c) 60 J
(d) 40 J
Q.13. A particle A suffers an oblique elastic collision with a particle B that is at rest initially. If their masses are the same, then after collision
(a) they will move in opposite directions
(b) A continues to move in the original direction while B remains at rest
(c) they will move in mutually perpendicular directions
(d) A comes to rest and B starts moving in the direction of the original motion of A
Q.14. A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is
(Take g = 10 ms-2)
(a) 20 ms-1 (b) 28 ms-1
(c) 10 ms-1 (d) 14 ms-1
Q.15. A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If e = coefficient of restitution, then what will be the ratio of velocity of two balls after collision?