The final velocity of a body, having initial velocity u. undergoing head on collision with another body of equal mass and initial velocity u, is--------=
Answers
Explanation:
Final velocity of first body (of mass m) is
V
1
=(
m
1
+m
2
m
1
−m
2
)u
1
+(
m
1
+m
2
2m
1
)u
2
=(
m+2m
m−2m
)50+(
m+2m
2×2m
)(−40)
=−
3
50
−
3
160
=−
3
210
=−70m/s
Final velocity of second body of mass 2m is
V
2
=(
m+2m
2m
)(50)+(
m+2m
2m−m
)(−40)
=
3
2
(50)+
3
1
(−40)
=
3
100
−
3
40
=
3
60
=20m/s
(ii) Ratio of final to initial kinetic energies for body of mass mis
2
1
m
2
v
1
2
2
1
m
1
v
1
2
=
u
2
u
1
v
1
2
=
(50)
2
(−70)
2
=
2500
4900
=
25
49
=Ant[log49−log25]
=Ant(1.6902−1.3979)
=Ant(0.2923)
=1.96
(iii) m
1
=1kg
m
2
=2kg
∴ Change in momentum of first body is m
1
v
1
−m
1
u
1
=m
1
(v
1
−u
1
)
=1(−70−50)=−120kgm/s
Change in momentum of second body is
m
2
v
2
−m
2
u
2
=m
2
(v
2
−u
2
)=2(20(−40))
=+120kgm/s
(iv) Momentum of the system will be conserve so change will be zero.