Two balls marked 1 and 2 of the same mass m and a third ball marked 3 of mass M are arranged over a smooth horizontal surface as shown in the figure. Ball 1 moves with a velocity v1 towards balls 2 and 3. All collisions are assumed to be elastic. If M < m, the number of collisions between the balls will be
Two balls marked 1 and 2 of the same mass m and a third ball marked 3 of mass M are arranged over a smooth horizontal surface as shown in the figure. Ball 1 moves with a velocity v1 towards balls 2 and 3. All collisions are assumed to be elastic. If M < m, the number of collisions between the balls will be
The correct option is B Two
The first collision will be between balls 1 and 2. Since both have the same mass, after the collision ball 1 will come to rest and ball 2 will move with speed v1. This ball will collide with the stationary ball 3. After this second collision, let v2 and v3 be the speeds of balls 2 and 3 respectively. Since the collisions are elastic, v2 and v3 are given by
v2=(m−Mm+M)v1 ...... (i)
and v3=(2mm+M)v1 ...... (ii)
If M < m, it follows from (i) and (ii) that v2<v3 and both have the same direction. Therefore, ball 2 cannot collide with ball 3 again. Hence, there are only two collisions and the correct choice is (b).
Two
The first collision will be between balls 1 and 2. Since both have the same mass, after the collision ball 1 will come to rest and ball 2 will move with speed v1. This ball will collide with the stationary ball 3. After this second collision, let v2 and v3 be the speeds of balls 2 and 3 respectively. Since the collisions are elastic, v2 and v3 are given by
v2=(m−Mm+M)v1 ...... (i)
and v3=(2mm+M)v1 ...... (ii)
If M < m, it follows from (i) and (ii) that v2<v3 and both have the same direction. Therefore, ball 2 cannot collide with ball 3 again. Hence, there are only two collisions and the correct choice is (b).
