The figure shows a string of equally placed beads of mass m, separated by a distance d . The beads are free to slids without friction on a thin wire . A constant force F acts on the first bead initially at rest till makes collision with second bead . The second bead then collides with the third and so on . Suppose that all collisions are elastic in nature :

Options

A. Speed of the first immediately before and immediately after its collision with the second bead is `sqrt((2Fd)/(m))` and zero respectively
B. Speed of the first bead immediately before and immediately after its collision with the second bead is `sqrt((2Fd)/(m))` and `(1)/(2) sqrt((2Fd)/(m))` respectively
C. Speed of the second bead immediately after collision with third bead is zero
D. The average speed of the first bead is `(1)/(2)sqrt(2Fd)/(m)`

Answer

A, C

Explanation

In elastic head on collision if the masses of the collision bodies are eaqual, the velocities after for `Ist` bead, `Fd = (1)/(2) m u^(2) rArr u = sqrt((2Fd)/(m))`