`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. (a) `(3/4)^(n-1)sqrt(5gr)`
B. (b) `(4/3)^(n-1)sqrt(5gr)`
C. (c) `(3/2)^(n-1)sqrt(5gr)`
D. (d) `(2/3)^(n-1)sqrt(5gr)`

Answer

A

Explanation

Velocity of second ball
`=((m//2-m)/(m//2+m))(0)+((2xxm)/(m+m//2))v`
`=4/3v`
Velocity of third ball will become,
`4/3t imes4/3v` or `(4/3)^2v`
`:. v_n=(4/3)^(n-1)v=sqrt(5gr)`
`:. v=(3/4)^(n-1)sqrt(5gr)`