Question

Two balls A (2 kg) and B (4 kg) move towards each other and after collision moves backwards. If the initial velocities of A and B were 2 m/s and 4 m/s, respectively, then what could be their respective final velocities?

a.8 m/s and 1 m/s
b.2.5 m/s and 3 m/s
c. 4 m/s and 2 m/s
d.5 m/s and 2.5 m/s​

Answer 1

Answer:

a) By momentum conservation,

2(4)−4(2)=2(−2)+4(ν

2

)

⟹ν

2

=1m/s.

b) e=

Velocityofapproach

Velocityofseparation

=

4−(−2)

1−9−2)

=

6

3

=0.5

c) At the maximum deformed state, by conservation of momentum, common velocity is ν=0

J

D

=m

2

(ν−u

2

)=4[(0−(−2)]=8Ns

d) Potential energy at the maximum deformed state,

U= loss in kinetic energy during defirmation

or U=(

2

1

m

1

u

1

2

+

2

1

m

2

u

2

2

)−

2

1

(m

1

+m

2

)ν

2

=(

2

1

2(4)

2

+

2

1

4(2)

2

)−

2

1

(2+4)(0)

2

=24J

e) J

R

=m

2

(ν

2

−ν)=4(1−0)=4Ns

also J

R

=eJ

D

=0.5×8=4Ns