Question

A uniform chain of length $l$ and mass $m$ lies on a smooth horizontal table with its length perpendicular to the edge of the table and small part overhanging. The chain starts sliding down from rest due to the weight of hanging part. The acceleration and velocity of the chain when length of the hanging portion is $x$

• A. $\frac{gx}{l},\sqrt{\frac{g{x}^2}{l}}$
• B. $\frac{gx}{l},\sqrt{gx}$
• C. $\frac{gx}{l},\sqrt{gl}$
• D. $\frac{gx}{l},\sqrt{g(l-x)}$

Answer 1

The correct option is A $\frac{gx}{l},\sqrt{\frac{g{x}^2}{l}}$

F when hanging length is $x=\frac{mx}{L}.g$

$acc=\frac{F}{m}=\frac{gx}{l}=\frac{dv}{dt}=\frac{dv}{dx}.v$

$\Rightarrow \frac{v^2}{2}=\frac{g{x}^2}{2l}$

$\Rightarrow v=\sqrt{\frac{g{x}^2}{L}}$