Question

A flexible but inextensible chain of length $l$ and weight $w$ N/m is held on a smooth table with an initial overhang 'a' as shown in figure. What will be the velocity $v$ with which the chain will leave the table if released?

• A. $v=\sqrt{\frac{g}{l}(l^2+a^2})$
• B. $v=\sqrt{gl}$
• C. $v=\sqrt{\frac{g}{l}\left(a^2\right)}$
• D. $v=\sqrt{\frac{g}{l}(l^2-a^2})$

Answer 1

The correct option is D $v=\sqrt{\frac{g}{l}(l^2-a^2})$

Using conversion of energy,

Initial kinetic energy + Initial potential energy = Final kinetic energy + final potential energy

$0-\left(wa\right)\times \frac{a}{2}=\frac{1}{2}\times \left(\frac{w\times l}{g}\right)v^2-\left(wl\right)\frac{1}{2}$

$\frac{w}{2}(l^2-a^2)=\frac{1}{2}\times \left(\frac{w\times l}{g}\right)v^2\Rightarrow v=\sqrt{\frac{g}{l}(l^2-a^2)}$