First slide

Elastic Modulie

Question

A wire is suspended vertically from a rigid support. When loaded with a steel weight in air, the wire extends by 16 cm. When the weight is completely immersed in water, the extension is reduced to 14 cm. The relative density of the material of the weight is

Moderate

A

2 g ${cm}^{- 3}$
B

6g ${cm}^{- 3}$
C

8 g ${cm}^{- 3}$
D

16 ${cm}^{- 3}$

Solution

Y = $\frac{Fl}{a ∆ l}; Y, l and a are constants$
$F \infty ∆ l$
In the first case V $ρg= 16$
In the second case,
( $ρg - V \times 1 \times g) \infty 14$
Dividing, $\frac{Vg (ρ - 1)}{Vgρ} = \frac{14}{18} = \frac{7}{8}$
or $\frac{ρ - 1}{ρ} = \frac{7}{8} or 8 ρ - 7 ρ or ρ = 8 g {cm}^{- 3}$

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