A uniform chain of mass m and length ℓ lies with two-thirds of its length on a table and one-third hanging. Find the work required to pull the hanging part back onto the table.
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Question

A uniform chain of mass m and length ℓ lies with two-thirds of its length on a table and one-third hanging. Find the work required to pull the hanging part back onto the table.

G1 Physics · Accepted Answer

The hanging part has length ℓ/3 and mass m/3. Its centre of mass is ℓ/6 below the tabletop. Work required to lift it onto the table is (m/3)g(ℓ/6)=mgℓ/18.