First slide

Elastic behaviour of solids

Question

When a certain weight is suspended from a long uniform wire, its length increases by 1 cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increases in length will be

Moderate

A

0.5 cm
B

2 cm
C

4 cm
D

8 cm

Solution

$\begin{array}{l} Y = \frac{Fl}{aΔl} or Δl \propto \frac{1}{a}; Δl \propto \frac{1}{D^{2}} \\ \frac{{Δl}_{2}}{{Δl}_{1}} = \frac{D_{1}^{2}}{D_{2}^{2}} = 4 or {Δl}_{2} = 4 {Δl}_{1} = 4 cm \end{array}$

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