Question

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v₁ while body B is at rest before collision. The velocity of the system after collision is v₂. The ratio v₁ : v₂ is :

• A. 1 : 2
• B. 2 : 1
• C. 4 : 1
• D. 1 : 4

Answer 1

The Correct Option is B

Step 1: Apply the Law of Conservation of Momentum

For a completely inelastic collision, the two bodies stick together after the collision. Using the law of conservation of momentum:

$$ m v_1 + m \cdot 0 = (m + m) v_2 $$

Step 2: Simplify the Equation

Rearranging:

$$ v_1 = 2 v_2 $$

Step 3: Determine the Ratio

The ratio of the velocities is:

$$ v_1 : v_2 = 2 : 1 $$