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A small ball of mass 'm' is connected by...

A small ball of mass `'m'` is connected by an intextensible mass less string of length `('l' = 10m)` with an another ball of mass `M = 4m`. They are released with zero tension in the string from a height `h(h = 5m)` as shown. Find the time when the string becomes taut for the first time after the mass `'M'` collides with the ground is _____`S`. (Take all collisions to be elastic) `(g = 10 m//s^(2))`

Text Solution

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The correct Answer is:
1
Just after collision velocities of both the balls will be `sqrt(2gh)` in opposite direction. Relative acceleration between the two ball is zero and relative velocity of approach is `2sqrt(2gh)`.
Hence they will collide after a time `t = (l)/(2sqrt(2gh))` At the time of collision of two balls relative velocity of approach `=` relative velocity of separate `= 2 sqrt(2gh)`
Hence string becomes tigt after the same time
`t = (l)/(2 sqrt(2gh))`
Hence the total time will be `(2t) = (l)/(2sqrt(2 gh)) = 1s`
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