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The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

Asked in AIEEE 2005 · Energy stored and maximum compression

• (1) zero
• (2) (ML²)/K
• (3) √MK L
• (4) (KL²)/(2M)

Step-by-step solution

Why the other options are wrong

• (1) Comes from looking only at the instant of maximum compression, when the block is momentarily at rest; it regains its speed as the spring relaxes.
• (2) No single slip gives this; it does not even have the dimensions of momentum.
• (4) Comes from dividing the spring energy by the mass; that is v²/2, not a momentum.

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