Sankalp NEET Full Test-1 Question-24 Solution

Question: 24. Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v_{1} while body B is at rest before collision. The velocity of the system after collision is v_{2}. The ratio v_{1}: v_{2} is :

(1) 1: 2

(2) 2: 1

(3) 4: 1

(4) 1: 4

Answer: Option (2)

Explanation:

Let the mass of each body be m.

Before collision, body A moves with velocity v_{1} and body B is at rest.

Initial momentum of the system is

p_{\text{initial}} = mv_{1} + m \times 0 = mv_{1}

In a completely inelastic collision, the two bodies stick together after collision.

Total mass after collision becomes 2m

and the common velocity is v_{2}.

Final momentum of the system is

p_{\text{final}} = 2m v_{2}

Using conservation of linear momentum,

mv_{1} = 2m v_{2}

Dividing both sides by m,

v_{1} = 2v_{2}

Therefore, the ratio is

v_{1} : v_{2} = 2 : 1

Hence, the correct answer is Option (2).