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Question: A uniform chain has a mass m and length l. It is held on a frictionless table with one-sixth of its ...

A uniform chain has a mass m and length l. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is :

A

mgℓ72\frac { \ell } { 72 }

B

C

mgℓ12\frac { \mathrm { mg } \ell } { 12 }

D

mgℓ6\frac { \mathrm { mg } \ell } { 6 }

Answer

mgℓ72\frac { \ell } { 72 }

Explanation

Solution

W = mgℓ2 m2\frac { \mathrm { mg } \ell } { 2 \mathrm {~m} ^ { 2 } } = mgℓ2(6)2\frac { \mathrm { mg } \ell } { 2 ( 6 ) ^ { 2 } } = mgℓ72\frac { \mathrm { mg } \ell } { 72 }