A hollow circular tube of radius R and negligible internal diameter is fixed on horizontal surface ball A of mas m is given velocity `v_(o)` in the shown direction. It collides with ball B of mass `2 m`. Collision is perfectly elastic. If centre of loop is origin of co-ordinates system, then co-ordinate of next collision is

Options

A. `((sqrt3)/(2)R, (- R)/(2))`
B. `((- sqrt3)/(2)R, (R )/(2))`
C. `((R )/(2), (- sqrt3)/(2)R)`
D. `((R )/(2), (R )/(2))`

Answer

C

Explanation

`-mv_(o) + o = mv_(1) + 2mv_(2)`
`-v_(o) = v_(1) + 2v_(2)`….(i) & `e = (v_(2) - v_(1))/(-v_(o)) = 1`
`:. V_(2) - v_(1) = -v_(o)`…. (ii) from (i) & (ii) `v_(1) = (v_(o))/(3), v_(2) = (-2v_(o))/(3)`
`:. T = (2piR)/(v_(o))`
Angle rotated by by `A = (2pi)/(3)`, Angle rotated by `B = (4pi)/(3)`rad.