# 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...

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

j. v′2=v1/4

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### 1 Answer

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'

(1/2)10v1^2=(1/2)v,'^2+(1/2)v2'^2

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.