Question

The coefficient of restitution e for a perfectly inelastic collision is:
(A) $1$
(B) $0$
(C) $\infty $
(D) $ - 1$

Answer 1

Hint: The coefficient of restitution is a measure of the restitution of a collision between two object: how much of the kinetic energy remains for an object to rebound or bounce back from one another versus how much is the loss of heat while rebounding, or work done in reforming an object.

Complete step by step answer:
The coefficient of restitution(e), is a measure of bounciness of collision between two objects. How much kinetic energy remains for the object to rebound from one another versus how much is lost as heat, or work done deforming the objects. The coefficient is defined as the ratio of relative speed after and before an impact, taken along the line of impact:
$e = \dfrac{{speed\,of\,seperation}}{{speed\,of\,approach}}$
The bodies stick together in perfectly inelastic collisions and move together hence velocity of separation is zero.
(i) for perfectly elastic collision $e = 1$
(ii) for a perfectly inelastic collision $e = 0$
(iii) for other collisions $0 < e < 1$
Therefore, the correct answer is (B) $0$

So, the correct answer is “Option B”.

Additional Information:
The coefficient of restitution depends to a large extent on the nature of two materials of which the colliding objects are made. It is also affected by the velocity, the shape and the size of colliding objects, the location of colliding objects at which the collision occurs and their temperatures.

Note:
Elastic collision is defined as encounters between two bodies in which the total kinetic energy of two bodies after an encounter is equal to their total kinetic energy before the encounter. Elastic collision occurs only if there is no net conversion of kinetic energy into another form and inelastic collision is defined as a collision in which kinetic energy is not conserved due to action of internal friction. In collision of macroscopic bodies, all kinetic energy is converted into vibrational energy of the atoms, causing heating effect and bodies are deformed.