1.

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

Answer»

`((sqrt3)/(2)R, (- R)/(2))`
`((- sqrt3)/(2)R, (R )/(2))`
`((R )/(2), (- sqrt3)/(2)R)`
`((R )/(2), (R )/(2))`

Solution :`-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.


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