A particle of mass m moving with a velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ establishing a contact with it for extremely small time $T$. Their force of contact increases from zero to $F_0$ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from $F_0$ to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by $F_0$ is
A particle of mass m moving with a velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ establishing a contact with it for extremely small time $T$. Their force of contact increases from zero to $F_0$ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from $F_0$ to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by $F_0$ is
$\frac{{mu}}{T}$
$\frac{{2mu}}{T}$
$\frac{{4mu}}{{3T}}$
$\frac{{3mu}}{{4T}}$
A particle of mass m moving with a velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ establishing a contact with it for extremely small time $T$. Their force of contact increases from zero to $F_0$ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from $F_0$ to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by $F_0$ is
Change in momentum = Impulse
= Area under force-time graph
$mv = $Area of trapezium
$⇒$ $mv = \frac{1}{2}\left( {T + \frac{T}{2}} \right)\;{F_0}$
$⇒$ $mv = \frac{{3T}}{4}{F_0}$ $⇒$ ${F_0} = \frac{{4mu}}{{3T}}$
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