Question

1) Which of the following equations represents momentum conservation?

a) ½ m₁v₁² + ½ m₂v₂² = ½ m₁v₁’² + ½ m₂v₂’². b) m₁v₁ +m₂v₂ = m₁v₁’ + m₂v₂’.

c) ¼ mv₁² = ½ ( ½ mv₁²).     d) m₁v₁ + m₂v₂ = ½ m₁v₁’² + ½ m₂v₂’².

2)Which of the following equations represents energy conservation?

a) ½ m₁v₁² + ½ m₂v₂² = ½ m₁v₁’² + ½ m₂v₂’². b) m₁v₁ +m₂v₂ = m₁v₁’ + m₂v₂’.

c) ¼ mv₁² = ½ ( ½ mv₁²). d) m₁v₁ + m₂v₂ = ½ m₁v₁’² + ½ m₂v₂’².

3) Which of the following equations represents momentum conservation for a completely inelastic collision?

a) ½ m1v12 + ½ m2v22 = ½ m1v1’2 + ½ m2v2’2. b) m1v1 +m2v2 = m1v1’ + m2v2’ c) ¼ mv12 = ½ ( ½ mv12).    d) m1v1 + m2v2 = (m1 + m2)v2’.

  

Answer 1

1)

As you know momentum of the particle

P=MV. Here M is mass and V is Velocity.

When two particle collide of mass m1 and m2

Velocity before collision v1 & v2 after collision v1' and v2'

Then conservation of momentum

Momentum before collision is equal momentum after collision.

m1v1+m2v2 =mv1'+mv2'

Correct answer is (b).

2)

As you know kinetic energy of the particle of mass M and velocity V

K =MV^2/2

In elastic collision kinetic energy is conserved.

Kinetic energy before collision is equal to after collision.

m1v1^2/2. +m2v2^2/2 =m1v1'^2/2 +m2v2'^2/2

Correct answer is (a)

3)

in inelastic collision particles after collision stick together.

So

Conservation of momentum will be

m1v1+m2v2=(m1+m2)v2'

Correct answer is (d).