The statement that the speed of the two balls after the collision is 0 is incorrect.
Yes, if the two balls stick together after the collision, their speed will be 0. Here's why:
Conservation of Momentum:
In a closed system like this collision, the total momentum before the collision is equal to the total momentum after the collision. This can be written as:
m1v1 + m2v2 = (m1 + m2)v_final
where:
m1 and m2 are the masses of the balls
v1 and v2 are their respective velocities before the collision
v_final is their combined velocity after sticking together
Substituting the values:
m1 = m
m2 = 2m
v1 = v
v2 = v/2
v_final is what we want to find
Plugging these values into the equation, we get:
mv + (2m)(v/2) = (m + 2m)v_final
mv + mv = 3mv_final
2mv = 3mv_final
v_final = 2mv / 3mv
v_final = 2/3
However, the question states that the two balls are stuck together. This means that the combined mass (m + 2m) will move as a single object after the collision.
Therefore, the speed of the single object after the collision will be:
v final = (2mv) / (3mv) = 2/3 * v
Since v is the speed of the first ball before the collision, which is not equal to 0, we can conclude that v_final is not equal to 0.
Therefore, the statement that the speed of the two balls after the collision is 0 is incorrect.