MHT CET · Physics · Center of Mass Momentum and Collision

A block of mass ‘m’ moving on a frictionless surface at speed ‘v’ collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle ‘θ’ with its initial direction and has speed ‘ $v_{1}$ ’ . The speed of the second block after collision is

A $\sqrt{v_{1}^{2} - v^{2}}$
B $\sqrt{v^{2} - v_{1}^{2}}$
C $\sqrt{v^{2} + v_{1}^{2}}$
D $\sqrt{v - v_{1}}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\sqrt{v^{2} - v_{1}^{2}}$

Step-by-step Solution

Detailed explanation

Applying law of conservation of kinetic energy,
KE (before collision) = KE (after collision)
$\frac{1}{2} m v^2+\frac{1}{2} m(0)^2=\frac{1}{2} m v_1^2+\frac{1}{2} m v_2^2$
$\Rightarrow v^2=v_1^2+v_2^2 \Rightarrow v_2=\sqrt{v^2-v_1^2}$
Thus, the velocity of second block after collision is $\sqrt{v^2-v_1^2}$.

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 block of mass ‘m’ moving on a frictionless surface at speed ‘v’ collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle ‘θ’ with its initial direction and has speed ‘ v 1 ’ . The speed of the second block after collision is

Step-by-step Solution

A block of mass ‘m’ moving on a frictionless surface at speed ‘v’ collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle ‘θ’ with its initial direction and has speed ‘ $v_{1}$ ’ . The speed of the second block after collision is