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Ball A of mass m strikes a stationaty ball B of mass M and undergoes an elastic collision.After collision ball a has a speed one-third of its initial speed.The ratio of M/m is a.1/4 b.1/2 c.2 d.4

Ball A of mass m strikes a stationaty ball B of mass M and undergoes an elastic collision.After collision ball a has a speed one-third of its initial speed.The ratio of M/m is


a.1/4


b.1/2


c.2


d.4

Grade:12th Pass

2 Answers

Swapnil Saxena
102 Points
9 years ago

Let the initial velocity of the body of mass m is V.

After collison , it became V/3.

Applying law of conservation of momentum

mV = mV/3 +MVo(Say)

(Assumption: the direction of the velocity doesnt changes after collison , otherwise not specified)

Then Vo = 2mV/3M----(1)

If the collison is Elastic, then energy remain conserved

=1/2(mV2) = 1/2(m(V/3)2+ MVo2)

=(mV2) = (m(V/3)2+ MVo2)

=8/9(mV2) =  MVo2

Substituting value of Vo

= 8/9(mV2) =  M(4m2V2/9M2)

= 8(m) =  (4m2/M)

= M/m= (1/2)

Note: After collison Speed becomes 1/3 has an incomplete meaning. Direction of ball A should also be specified)

ankitesh gupta
63 Points
8 years ago

 

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