First slide

Work done by Diff type of forces

Question

A uniform chain of mass ‘m’ and length l is on a table with $\frac{1}{4}$ of its length hanging freely from the edge of the table. The amount of work done is dragging the chain on to the table completely is

Moderate

A

mgl
B

$\frac{m g l}{8}$
C

$\frac{m g l}{32}$
D

$\frac{m g l}{16}$

Solution

$W_{e x t} + W_{g r} = Δ K . E = 0$
$W_{e x t} = - W_{g r} = - [- Δ V] = Δ V$
$\Rightarrow W_{e x t} = V_{f} - V_{i}$
We also know $V = m g l_{C O M}$

So, $V_{i} = - \frac{m}{4} . g . \frac{l}{8} = - \frac{m g l}{32}$
$V_{f} = 0$
$W_{e x t} = \frac{m g l}{32}$

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