Question

A uniform rope of linear density d and length l hanging from the edge of table .the work done in pulling the rope on to the table is?

Answer 1

Answer:dgl^2/2

Explanation:

Answer 2

Given :

Length of hanging rope :

= l

Linear density of the hanging rope :

=d

To find :

Work done in pulling the rope on the table = ?

Solution :

∴Mass of the rope m will be :

m =$d\times l$

The forcing acting will be the weight of the rope which is :

= mg

=$dlg$

We know that formula for work done is :

W= ∫$F.dx$

So according the above formula the work in moving the rope on the table will be :

$W=\int\limits^l_o {Fl} \, dl \\\\W=\int\limits^l_0 {dlg} \, dl\\\\W= dg\frac{l^{2} }{2}$

So finally the work done in moving the rope on the table is :

W=$dg\frac{l^{2} }{2}$