SATHEE: Properties Of Solids And Liquids Question 555

Properties Of Solids And Liquids Question 555

Question: When a building is constructed at $- 10^{\circ} C$ , a steel beam (cross-sectional area $45 c m^{2}$ ) is put in place with its ends cemented in pillars. If the sealed ends cannot move, what will be the compressional force in the beam when the temperature is $25^{\circ} C$ ? For this kind of steel, $α = 1.1 \times 10^{- 5}^{o} C^{- 1}$ and $Y = 2.0 \times 10^{11} N / m^{2}$ .

Options:

A) $2.5 \times 10^{3} N$

B) $3.5 \times 10^{5} N$

C) $2.5 \times 10^{5} N$

D) $3.5 \times 10^{3} N$

Show Answer

Answer:

Correct Answer: B

Solution:

$\frac{Δ L}{L_{0}} = α Δ T = (1.1 \times 10^{- 5}^{o} C^{- 1}) (35^{o} C)$

$[∵ Δ L = L_{0} α Δ T]$ where, $Δ L =$ Change in length and $L_{0} =$ original length $= 3.85 \times 10^{- 4}$ So, $F = Y A \frac{Δ L}{L_{0}}$

$[∵ {Young}^{'} s modulus, Y = \frac{F / A}{Δ L / L_{0}}]$

$= (2.0 \times 10^{11} N / m^{2})$

$(45 \times 10^{- 4} m^{2}) (3.85 \times 10^{- 4})$

$= 3.5 \times 10^{5} N$

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