Question

A particle of mass 'm' collides with another stationary particle of mass 'M'. A particle of mass 'm' stops just after collision. The coefficient of restitution is ______.

विकल्प

• M/m

• m/M

• `(M-m)/(M+m)`

• `(m+M)/m`

Answer 1

A particle of mass 'm' collides with another stationary particle of mass 'M'. A particle of mass 'm' stops just after collision. The coefficient of restitution is m/M.

Explanation:

According to conservation of linear momentum

Mu + 0 = Mv + 0

u and v are respective initial and final velocities of m and M

`therefore e="v"/"u"="m"/"M"`

OR

Let u₁ be the initial velocity of 'm' and its velocity after collision v₁ = 0. For mass 'm' initial velocity u₂ = 0. By law of conservation of momentum

mu₁ =Mv₂

`thereforem/M="v"_2/"u"_1`

Coefficient ofrestitution `=("v"_2-"v"_1)/("u"_1-"u"_2)="v"_2/"u"_1`