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 i s_______. (Take g = 10 m/s²)
Physics · Work , Power and Energy · conservation of mechanical energy
JEE Mains 2021

Question

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 i s_______. (Take g = 10 m/s²)

Physics · Work , Power and Energy · conservation of mechanical energy

JEE Mains 2021

G1 Physics · Accepted Answer

The chain has linear density 1 kg/m. Initially only 1 m hangs, with PE=-(1 kg)g(0.5 m)=-5 J relative to the tabletop. When fully vertical, the 3 kg chain has CM 1.5 m below the table, PE=-45 J. The decrease 40 J becomes kinetic energy, so k=40 J.