Question

A bullet of mass 10g moving with a velocity of 400 m/s gets embedded in a freely suspended wooden block of mass 490 g. Find the velocity acquired by the block.

Answer 1

Given,

Mass of bullet = 10g

Velocity of bullet = 400 m/s

Mass of wooden block = 490g

To Find,

velocity acquired by the block.

Solution,

Let the final velocity acquired by the block be 'v m/s'.

The mass of the bullet = m₁ = 10 g = 0.01 kg

The mass of the wooden block= m₂ = 490 g = 0.49 kg

Also, the initial velocity of the bullet is given by= u₁ = 400 m/s

The initial velocity of the wooden block is given by = u₂ = 0 m/s

(Here, all of the physical quantities are converted to SI units)

Now, the momentum conservation of law states that;

Momentum before collision = Momentum after collision

⇒ (m₁ × u₁) + (m₂ × u₂) = (m₁ + m₂) × v

⇒ v = (m₁ × u₁) + (m₂ × u₂) / (m₁ + m₂)

⇒ v = (0.01 × 400) + (0.49 × 0) / (0.01 +0.49) m/s

⇒ v = (4+0) / 0.5 m/s

⇒ v = 8 m/s

Hence, v = 8 m/s which means this is the velocity acquired by the block.