First slide

Elastic behaviour of solids

Question

A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

Moderate

A

l
B

2l
C

$\frac{l}{2}$
D

$\frac{l}{4}$

Solution

$\begin{array}{l} l = \frac{FL}{AY} = \frac{FL}{{πr}^{2} Y} ∴ l \propto \frac{FL}{r^{2}} (Y = constant) \\ ∴ \frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \times \frac{L_{2}}{L_{1}} {(\frac{r_{1}}{r_{2}})}^{2} = 2 \times 2 \times {(\frac{1}{2})}^{2} = 1 \end{array}$
$∴ l_{2} = l_{1} i.e. increment in its length will be l .$

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