Physics Q17 – NEET-UG 2024

Home Physics Units & MeasurementsQuestion #564

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 :

Clue 1 of 3: Collision Type

Identify the type of collision described in the problem to determine which physical quantities are conserved.

🧠 Full Solution Path

Step 1: Identify Collision Type and Principle✦ Active

The problem describes a 'completely inelastic one dimensional collision'. In such a collision, the two bodies stick together after impact and move as a single unit. The principle of conservation of linear momentum applies.

Step 2: Apply Conservation of Momentum○ Expand

Let the mass of body A be $m_{A} = m$ and the mass of body B be $m_{B} = m$ (since they are of same mass). The initial velocity of body A is $u_{A} = v_{1}$ and body B is at rest, so $u_{B} = 0$ . After the collision, the bodies stick together and move with a common velocity $v_{f i n a l} = v_{2}$ . According to the conservation of momentum:

m_{A} u_{A} + m_{B} u_{B} = (m_{A} + m_{B}) v_{f i n a l}

m v_{1} + m (0) = (m + m) v_{2}

m v_{1} = 2 m v_{2}

💡 Teacher's Secret Hint

Remember that in a completely inelastic collision, the final mass is the sum of the individual masses, and they share a common final velocity.

Step 3: Calculate the Ratio

v_{1} : v_{2}

○ Expand

From the momentum conservation equation, we have:

m v_{1} = 2 m v_{2}

Divide both sides by $m$ (assuming $m \neq 0$ ):

v_{1} = 2 v_{2}

To find the ratio $v_{1} : v_{2}$ , rearrange the equation:

\frac{v_{1}}{v_{2}} = \frac{2}{1}

Thus, the ratio $v_{1} : v_{2}$ is $2 : 1$ .

💡 Teacher's Secret Hint

Always simplify the equation to its simplest form before determining the ratio.

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Physics Question 17 – NEET-UG 2024

Clue 1 of 3: Collision Type

🧠 Full Solution Path