First slide

Elastic Modulie

Question

Two wires of diameter 0.25 cm, one made of steel and other made of brass are loaded as shown in figure. The unloaded length of the steel wire is 1.5 m and that of brass is 1.0 m. Young's modulus of steel is 2.0 x $10^{11}$ Pa and that of brass is 1.0 x $10^{11}$ Pa. The ratio of elongations of steel and brass wires. ( $\frac{∆ l_{steel}}{∆ l_{brass}} = ?$ )

Moderate

A

1.25
B

l.5
C

2.0
D

0.5

Solution

$∆ l_{brass} = \frac{6 g \times 1.0}{A \times 1 \times 10^{11}}$
$∆ l_{steel} = \frac{10 g \times 1.5}{A \times 2 \times 10^{11}}$
$\frac{∆ l_{steel}}{∆ l_{brass}} = \frac{10 g \times 1.5}{A \times 2 \times 10^{11}} \times \frac{A \times 1 \times 10^{11}}{6 g \times 1.0}$
= $\frac{15}{12} = \frac{5}{4} = 1.25$

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