`n` elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius `r` as shown in the figure. The masses of the balls are `m`, `m/2`, `m/2^2`, …………….`(m)/(2^(n-1))` respectively. What is the minimum velocity which should be imparted to the first ball of mass `m` such that `n^th` ball completes the vertical circle

Options

A. `(3/4)^(n-1)sqrt(5gr)`
B. `(4/3)^(n-1)sqrt(5gr)`
C. `(3/2)^(n-1)sqrt(5gr)`
D. `(2/3)^(n-1)sqrt(5gr)`

Answer

A

Explanation

In head on elastic collison
`v_(1)^(') = (m//2-m)/(m//2+m)(0) + [(2(m))/(m//2+m]](v) = 4/3v`

Finally, `v_(n)^(') = (4/3)^(n-1).v = sqrt(5gr)`
`v= (3/4)^(n-1).sqrt(5gr)`