A small ball of mass `1kg` is released from a smooth horizontal pipe containing a spring fixed at a height of `20m` and `10m` away from a vertical wall as shown in the figure. The initial compression of a spring is `2cm` and it strikes a smooth vertical wall and smooth horizontal floor repeatedly and elastically as shown. The time period of one complete oscillation `(g = 10m//s^(2))`. (The ball do not collide with walls of the pipe ) is `P +(pi)/(50Q)`, the value of `Q -P` is__________

Answer

1

Explanation

`H = (1)/(2) gt^(2) rArr t = 2sec`
`V_(x) (4) = 20 rArr V_(x) = 5`
`(1)/(2) (1)(5)^(2) = (k)/(2) (2xx10^(-2))^(2)`
`k = 62500`
`T = 4 + pi sqrt((m)/(k))`