Question

What is the law of conservation of Momentum? A car of mass 200 kg moving with 3m/s collides with another car of mass 300 Kg moving in the same direction at 2 m/s .They collide and move with same velocity . What is the common velocity

Answer 1

Explanation:

Law of conservation of momentum is that law which states that total momentum before collision of two objects is always equal to total momentum after their collision.

Momentum = Mass × Velocity

Hence, according to law of momentum:-

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where, m₁ = mass of first body

            m₂ = mass of second body

            u₁ = initial velocity of first body

            u₂ = initial velocity of second body

            v₁ = final velocity of first body

            v₂ = final velocity of second body

Now,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

⇒ 200 kg · 3 m/s + 300 kg · 2 m/s = 200 kg · v₁ + 300 kg · v₂ [ " · " means multiply ]

⇒ 600 kg m/s + 600 kg m/s = 200 kg · v₁ + 300 kg · v₂

⇒ 1200 kg m/s = 200 kg · v₁ + 300 kg · v₂      

⇒ 1200 kg m/s = 200 kg · v₁ + 300 kg · v₁                                                                

[ According to question, velocity after colliding is same for both cars.

So,  v₁ = v₂ ]

⇒ 1200 kg m/s = v₁ (200 kg + 300 kg)

⇒ 1200 kg m/s = v₁ · 500 kg

Hence,

  $v = \frac{1200 kg m/s}{500 kg} = 2.4 m/s$

Therefore, common velocity of both cars is 2.4 m/s.