A particle of mass m collides head-on with another stationary particle of mass M such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restitution is e ?

Question

A particle of mass m collides head-on with another stationary particle of mass M such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restitution is e ? (A) e=0 (B) e=(m/M)≤ 1 (C) e=(m/M)≥ 1 (D) e=(M/m)≤ 1

Tardigrade Admin · Accepted Answer

The collision is not perfectly elastic or inelastic since when one is at rest the other is in motion with different velocities mu=Mv ⇒ (m/M)=(v/u) But e=(v/u)≤ 1 e=(m/M)≤ 1

Q. A particle of mass $m$ collides head-on with another stationary particle of mass $M$ such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restitution is $e$ ?

$e = 0$

$e = \frac{m}{M} \leq 1$

$e = \frac{m}{M} \geq 1$

$e = \frac{M}{m} \leq 1$

The collision is not perfectly elastic or inelastic since when one is at rest the other is in motion with different velocities
$m u = M v$
$\Rightarrow \frac{m}{M} = \frac{v}{u}$
But $e = \frac{v}{u} \leq 1$
$e = \frac{m}{M} \leq 1$

Q. A particle of mass m collides head-on with another stationary particle of mass M such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restitution is e ?

e=0

e=Mm​≤1

e=Mm​≥1

e=mM​≤1