Question

A uniform, long thin chain of length l, with one end attached to a horizontal axle of cross-sectional radius r(r <<l), is hung vertically down initially. The chain is then wound up slowly on the axle, doing an amount of work W₁. The chain is then cut into two equal parts (with length each) and the two parts are wound one after the other on the same axle doing an amount of work W₂ and W₃ respectively, The ratio is –

• A. 1
• B. $\frac { 1 } { 2 }$
• C. $\frac { 1 } { 4 }$
• D. 2

Answer 1

Answer: (D)

2

Answer 2

W₁ = mg $\frac { \ell } { 2 }$, W₂ = , W₃ = $\frac { \mathrm { m } } { 2 } \mathrm {~g} \frac { \ell } { 4 }$