First slide

Elastic behaviour of solids

Question

When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is

Moderate

A

1.2 cm
B

0.6 cm
C

0.3 cm
D

0.15 cm

Solution

$Y = \frac{Mg \times 4 \times l}{{πD}^{2} \times Δl} or Δl \propto \frac{1}{D^{2}}$
When D is doubled, $Δl$ becomes one-fourth, i.e.,
$\frac{1}{4} \times 2 .4 cm, i.e., 0 .6 cm . \times 2 .4 cm, i.e., 0 .6 cm$

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