Question #13429

a moving body A of mass 5kg collides with a stationary body B. If both the bodies move togeather with a speed of 1/3 that of the body A after collision, mass of B is

Expert's answer

Let Ia be the momentum of a moving body A before collision, Iab be the momentum of A and B after collision, Va the velocity of A before collision, Vab velocity of A and B after collision, Ma and Mb the masses of A and B respectively. Then

Ia = Ma*Va

Iab = (Ma+Mb)*Vab

Vab = Va/3

Ia = Iab

Ma*Va = (Ma+Mb)*Vab

Ma*Va = (Ma+Mb)*Va/3

Ma = (Ma+Mb)/3

Ma = Ma/3 + Mb/3

3*Ma = Ma + Mb

2*Ma = Mb

Mb = 2*5 = 10 kg

So, mass of B is 10 kg.

Ia = Ma*Va

Iab = (Ma+Mb)*Vab

Vab = Va/3

Ia = Iab

Ma*Va = (Ma+Mb)*Vab

Ma*Va = (Ma+Mb)*Va/3

Ma = (Ma+Mb)/3

Ma = Ma/3 + Mb/3

3*Ma = Ma + Mb

2*Ma = Mb

Mb = 2*5 = 10 kg

So, mass of B is 10 kg.

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