A small ball of mass `m` is connected by an inextensible massless string of length with an another ball of mass `M = 4m`. They are released with zero tension in the string from a height `h` as shown in the figure. Find the time when the string becomes taut for the first time after the mass `M` collides with the ground. Take all collisions to be elastic.

Answer

`l/sqrt(2gh)`

Explanation

Just after collision velocities of both the balls will be `sqrt(2gh)` in opposite directions. Relative acceleration between the two balls is zero and relative velocity of approach is `2sqrt(2gh)` hence they will collide after a time
`t=l/(2(2gh))` .........i
At the time of collision of two balls relative velocity of approach `=2sqrt(2gh)`
Hene relative velocity of separation will also be `2sqrt(2gh)` (collision is elastic). Hence the sting becomes tight after the some time
`t=l/(sqrt(2gh))`
Hence the total time will be `2t` or `1/sqrt((2gh))`