Kinetic energy loss in perfectly inelastic collision

Steps:

• Calculate initial KE for each trolley: trolley 1 (4 kg, 1 m/s) is ½×4×1² = 2 J; trolley 2 (2 kg, 2 m/s opposite) is ½×2×2² = 4 J; total initial KE = 6 J.
• Apply conservation of momentum: initial momentum = 4×1 + 2×(-2) = 0 kg m/s; total mass = 6 kg, so final velocity = 0 m/s.
• Calculate final KE: ½×6×0² = 0 J.
• KE lost = initial KE - final KE = 6 J - 0 J = 6 J.

Why B is correct:

• In a perfectly inelastic collision, objects stick together, so final KE uses common velocity from momentum conservation, yielding 6 J loss via ½mv² formula.

Why the others are wrong:

• A: Ignores contribution from second trolley's KE.
• C: Equals total initial KE, forgetting to subtract final KE.
• D: Overestimates by adding extraneous energy or misapplying velocities.

Final answer: B