The impact and deformation during collision may generate . . .

Question : The impact and deformation during collision may generate heat and sound. Part of the initial kinetic energy is transformed into other forms of energy. A useful way to visualize the deformation during collision is in terms of a 'compressed spring', If the 'spring' connecting the two masses regains its original shape without loss in energy, then the initial kinetic energy is equal to the final kinetic energy but the kinetic energy during the collision time Δt is not constant. Such a collision is called an elastic collision. On the other hand the deformation may not be relieved and the two bodies could move together after the collision. A collision in which the two particles move together after the collision is called a completely inelastic collision. The intermediate case where the deformation is partly relieved and some of the initial kinetic energy is lost is more common and is appropriately called an inelastic collision. If the initial velocities and final velocities of both the bodies are along the same straight line, then it is called a one-dimensional collision, or head-on collision. When two equal masses undergo a glancing elastic collision with one of them at rest, after the collision, they will move at right angles to each other.

(i) After collision when two particles moves together then collision is 

(a) Elastic collision

(b) Completely inelastic collision

(c) Both (a) and (b) 

(d) None of these.

(ii) In elastic collision, loss in kinetic energy is 

(a) Zero

(b) Positive

(c) Negative

(d) None of these

(iii) The coefficient of restitution for a perfectly elastic collision is 

(a) 1

(b) 0

(c) ∞

(d) -1

(iv) A body of mass M collides against a wall with a velocity of v and retraces its path with the same speed. The change in momentum is (take the initial direction of velocity as positive)

(a) 2Mv

(b) 1 Mv

(c) -2Mv

(d) Zero

Doubt by Riddhi

Solution : 

(i) After collision when two particles moves together then collision is 

(a) Elastic collision

(b) Completely inelastic collision

(c) Both (a) and (b) 

(d) None of these.

Ans : (b) Completely inelastic Collision.

Explanation : A completely inelastic collision is a type of collision in which the two colliding objects stick together after the collision. This means that their final relative velocity is zero. Completely inelastic collisions are the most extreme type of inelastic collision, in which the maximum amount of kinetic energy is lost.

(ii) In elastic collision, loss in kinetic energy is 

(a) Zero

(b) Positive

(c) Negative

(d) None of these

Ans: (a) Zero

Explanation : In an elastic collision, there is no loss of kinetic energy. Therefore, the final kinetic energy of the two particles must be equal to their initial kinetic energy.

(iii) The coefficient of restitution for a perfectly elastic collision is 

(a) 1

(b) 0

(c) ∞

(d) -1

Ans : (a) 1

Explanation : The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of the two particles after the collision to their relative velocity before the collision. For a perfectly elastic collision, the relative velocity of the two bodies after the collision is always equals to the relative velocities of the two bodies before the collision this is why  the coefficient of restitution for a perfectly elastic collision is always equal to 1.

(iv) A body of mass M collides against a wall with a velocity of v and retraces its path with the same speed. The change in momentum is (take the initial direction of velocity as positive)

(a) 2Mv

(b) 1 Mv

(c) -2Mv

(d) Zero

Ans : (b) -2Mv

Explanation : 

Mass of the body (M)

Initial velocity of the before collision = +v

Final velocity of the body after the collision = -v

Change in momentum

=Final Momentum - Initial Momentum

= m(-v) - m(v)

=-mv-mv

=-2mv