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 extermely small time. `T`. Their force of contact increases from zero to `F_0` linearly in time `T//4`, remains constant for a further time `T//2` and decreases linearly from `F_0` to zero in further time `T//4` as shown. The magnitude possessed by `F_0` is.
.

Options

A. `(m u)/(T)`
B. `(2 m u)/(T)`
C. `(4 m u)/(3 T)`
D. `( 3m u)/(4 T)`

Answer

C

Explanation

( c) Change in momentum = Impulse
= Area under force - time graph
:. `mv` = Area of trapezium
`rArr mv = (1)/(2) (T + (T)/(2)) F_0`
`rArr mv = (3T)/(4) F_0 rArr F_0 = (4 m u)/(3 T)`.