MHT CET · Physics · Center of Mass Momentum and Collision

A block of mass 'm' moving along a straight line with constant velocity \(3 \overrightarrow{\mathrm{V}}\) collides
with another block of same mass at rest. They stick together and move with
common velocity. The common velocity is

A \(\frac{3 \vec{v}}{2}\)
B \(2 \vec{V}\)
C \(\overrightarrow{3} \vec{V}\)
D \(\vec{V}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3 \vec{v}}{2}\)

Step-by-step Solution

Detailed explanation

A block of mass \('m'\) moving along a straight line with constant velocity \(3 \vec{v}\) collides with another block of same mass at rest. They stick together and move with common velocity. The common velocity is \(\frac{3 \vec{v}}{2}\).
\((m+m) v_{2}=m \times 3 v\)
\(v_{2}=\frac{3}{2} \vec{v}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A block of mass 'm' moving along a straight line with constant velocity \(3 \overrightarrow{\mathrm{V}}\) collideswith another block of same mass at rest. They stick together and move withcommon velocity. The common velocity is

Step-by-step Solution

A block of mass 'm' moving along a straight line with constant velocity \(3 \overrightarrow{\mathrm{V}}\) collides
with another block of same mass at rest. They stick together and move with
common velocity. The common velocity is