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. `(mu)/T`
B. `(2mu)/T`
C. `(mu)/(2T)`
D. None of these

Answer

B

Explanation

In one dimensional elastic collision, between two equal masses velocities are interchanged. Therefore, change in linear momentum of any of the particle will be mu. Now impulse or area under F-T graph gives the change in linear momenntum.

`therefore 1/2F_(0)T = mu`
or `F_(0) = (2mu)/(T)`