First slide

Stress and strain

Question

A wire is elongated by 2 mm when a brick is suspended from it. When the brick is immersed in water, the wire contracts by 0.6 mm. What is the density of brick ?

Moderate

A

$3333 k g / m^{3}$
B

$4210 k g / m^{3}$
C

$5000 k g / m^{3}$
D

$2000 k g / m^{3}$

Solution

$Δ l = \frac{F l}{A Y}$ ……(1)
$∴ \frac{Δ l^{'}}{Δ l} = \frac{F^{'}}{F} = \frac{m g - ρ_{ω} . V g}{m g} = \frac{m g - \frac{m}{ρ_{B}} . ρ_{ω} . g}{m g} = 1 - \frac{ρ_{ω}}{ρ_{B}}$
$∴ ρ_{B} = \frac{ρ_{ω}}{(1 - \frac{Δ l^{'}}{Δ l})} = 3333 k g / m^{3} .$

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