A particle of mass m moving with velocity u makes an elastic one-dimentional collision with a stationary particle of mass `m`. They come in contact for a very small time `t_0`. Their force of interaction increases from zero to `F_0` linearly in time `0.5t_0`, and decreases linearly to zero in further time `0.5t_0` as shown in figure. The magnitude of `F_0` is

Options

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

Answer

C

Explanation

Area under the force-time graph is impules, and impulse is change in momentum.
Area of graph=change in momentum
`implies 1/2 TF_(0)=2 m u implies F_(0)=(4m u)/(T)`.