Question
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 Fig. 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
Answer: Option B
:
B
The first collision will be between balls 1 and 2. Since both have the same mass, after the collision ball 1will 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 v2and v3 be the speeds of balls 2 and 3 respectively. Since the collisionsare elastic,v2 and v3 are given by (see Sec. 9)
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.
Thus the correct choice is (b).
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:
B
The first collision will be between balls 1 and 2. Since both have the same mass, after the collision ball 1will 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 v2and v3 be the speeds of balls 2 and 3 respectively. Since the collisionsare elastic,v2 and v3 are given by (see Sec. 9)
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.
Thus the correct choice is (b).
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