Consider the collision of two identical parti-
cles, with m1 = m2 = 10 g.
The initial velocity of particle 1 is v1 and
particle 2 is initially at rest, v2 = 0 m/s..
After an elastic head-on collision, the final
velocity of particle 2 is v′2 and given by?
a. v′2 = 0
b. v′2 = v1
c. v′2 =2 v1/3
d. v′2 =v1/2
e. v′2 =5 v1/3
f. v′2 =4 v1/3
g. v'2 = 2 v1
h. v′2 =3 v1/4
i. v′2 =v1/3
v'2 = v1 is the right answer. The choice b is correct.
A proof is given as follows:
By consevation of momentum and kinetic energy we obtain the following 2 equations.
10v1 = 10v1'+10v2'
Solve these simple two simultaneous equtions for v1'f and v2'f the final velocity of the first and 2nd particle.
Then we get the solutions: v1' = 0 and v2' = v1. That is ,two perfect elastic bodies, when one is at motion with a velocity of v1 collides with another other with equal mass body at rest, the first comes to rest imparting its entire velocity v1 to the 2nd.