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Grade: 12th pass

                        

A ball of mass 40gm impinges on a ball of mass 80 gm which is moving in the same direction as the first.If the coefficient of restitution is 3/4 and the first ball is reduced to rest after the impact find the ratio between the velocities of two ball before impact.

one month ago

Answers : (1)

Harsh
13 Points
							
Let the coefficient of restitution be e 
Newton's law of collision equation :              
0−u
2
​ 
 −0
​ 
 =−e ⟹v 
2
​ 
 =eu ............(1)
Applying conservation of momentum :
1
​ 
 u 
1
​ 
 +o=0+m 
2
​ 
 v 
2
​ 
 
∴ m 
1
​ 
 u=m 
2
​ 
 eu ⟹m 
1
​ 
 =em 
2
​ 
         ..............(2)
Initial kinetic energy of the system E 
i
​ 
 = 
2
1
​ 
 m 
1
​ 
 u 
1
2
​ 
 = 
2
1
​ 
 m 
1
​ 
 u 
2
           
 
Final kinetic energy of the system E 
f
​ 
 = 
2
1
​ 
 m 
2
​ 
 v 
2
2
​ 
 = 
2
1
​ 
 m 
2
​ 
 e 
2
 u 
2
 
 
Also loss in kinetic energy ΔE= 
2
1
​ 
 m 
1
​ 
 u 
2
 − 
2
1
​ 
 m 
2
​ 
 e 
2
 u 
2
 
   
2
1
​ 
 ( 
2
1
​ 
 m 
1
​ 
 u 
2
 )= 
2
1
​ 
 m 
1
​ 
 u 
2
 − 
2
1
​ 
 m 
2
​ 
 e 
2
 u 
2
 
  
2
1
​ 
 ( 
2
1
​ 
 m 
1
​ 
 u 
2
 )= 
2
1
​ 
 m 
1
​ 
 u 
2
 − 
2
1
​ 
 m 
1
​ 
 eu 
2
                       (using (2))
⟹e= 
2
1
​ 
25 days ago
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