Classical Mechanics - Elastic Collision

 

A uniform stick of length L and mass M lies on a frictionless horizontal surface. A point particle of mass m approaches the stick with speed v on a straight line perpendicular to the stick that intersects the stick at one end, as shown above. After the collision, which is elastic, the particle is at rest. The speed V of the center of mass of the stick after the collision is

A. m/Mv
B. m/(M + m)v
C. √(m/M)v
D. √[m/(M + m)]v
E. 3m/Mv

(GR8677 #44)

Solution:

Conservation of momentum (elastic collision):
m_A v_A + m_B v_B = m_A v_A' + m_B v_B'
mv + 0 = 0 + MV
V = m/Mv

Answer: A