First slide

Elastic Modulie

Question

A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm)

Moderate

A

l
B

2l
C

Zero
D

l /2

Solution

The situation is shown in fig

let L and A be the length and area of cross-section of the wire respectively.
For first case, $Y = \frac{W / A}{l / L}$ ……………..(1)
where Y is young's modulus of the material of the wire. If l 'be the elongation in the wire in second case, then
$Y = \frac{W / A}{2 l^{'} / L}$ ……………………………(2)
From equations (1) and (2), we get
$\frac{W / A}{l / L} = \frac{W / A}{2 l^{'} / L}$
or , $l = 2 l^{'} or l^{'} = l / 2$
So, total elongation of both sides $= 2 l^{'} = l$

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