Question

A particle of mass $m$ moving with velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$. They are in contact for a short time $T$. Their force of interaction increases from zero to $F_0$ linearly in time $\frac{T}{2}$ and decreases linearly to zero in further time $\frac{T}{2}$ (shown in figure). The magnitude of $F_0$ is

• A. mu/2 T
• B. mu/T
• C. 2mu/T
• D. None of these

Answer 1

Answer: (C)

In elastic one dimensional collision particle rebounds with same speed in opposite direction.
So, change in momentum $=2mu$
But, impulse $=F\times T=$ Change in momentum
$\Rightarrow F_0\times T=2mu$
or $F_0=\frac{2mu}{T}$