AP EAMCET · PHYSICS · Center of Mass Momentum and Collision

A particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$ , $M$ and $2 M$ . The equal masses move along $X$ - and $Y$ - axes with velocities $4 m s^{- 1}$ and $6 m s^{- 1}$ respectively. The magnitude of the velocity of the heavier mass is

A $\sqrt{17} m s^{- 1}$
B $2 \sqrt{13} m s^{- 1}$
C $\sqrt{13} m s^{- 1}$
D $\frac{\sqrt{13}}{2} m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\sqrt{13} m s^{- 1}$

Step-by-step Solution

Detailed explanation

Recall the condition of conservation of linear momentum in x-axis is, 0=M×4+0+2M×ucosθucosθ=2...1 and a vertical component, 0=0+6M+2Musinθusinθ=3...2 from equation 1 & 2…

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 particle of mass 4M which is initially at rest explodes into three pieces of masses M, M and 2M. The equal masses move along X- and Y- axes with velocities 4 m s-1 and 6 m s-1 respectively. The magnitude of the velocity of the heavier mass is

Step-by-step Solution

A particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$ , $M$ and $2 M$ . The equal masses move along $X$ - and $Y$ - axes with velocities $4 m s^{- 1}$ and $6 m s^{- 1}$ respectively. The magnitude of the velocity of the heavier mass is