A uniform chain of length 3 meter and mass 3 kg overhangs a smooth… | JEE Main 2021 (26 Aug, Shift 1)

Q26JEE Main 2021 · 26 AUG · SHIFT 1Medium

Conservation of Energy

A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter lying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is .................. (Take g = 10 m/s2)

Numerical answer type. Work it out, then open the answer.

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Answer: 40

Smooth table, so KE gained = loss of PE. Take the table top as zero; mass per metre $= 1\text{ kg/m}$ .
Initially 1 m (1 kg) hangs, CM 0.5 m below: $U_i = -1 \times 10 \times 0.5 = -5\text{ J}$ .
Finally all 3 m (3 kg) hangs, CM 1.5 m below: $U_f = -3 \times 10 \times 1.5 = -45\text{ J}$ .
$k = U_i - U_f = -5 + 45 = 40\text{ J}$

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