Question

09. A brass sheet is 40 cm long and 8 cm broad.
If the surface area is 320.1 cm2 at 100°C, co-
efficient of linear expansion of brass is:
(A) 15.5 x 10-7 / °C
(B) 155 x 10-7/°C
(C) 1.55 x 10-7 °C
(D) 1550 x 10-7, °c​

Answer 1

Correct question :

A brass sheet is 40 cm long and 8 cm broad at 0°C. If the surface area is 320.1 cm² at 100°C, find the coefficient of linear expansion of brass.

Answer :

Option - A $\sf{\implies{15.5\times{10}^{-7}/\degree{C}}}$

Explaination :

Surface area of sheet at 0°C, A₀ = 40 × 8 = 320 cm²

Surface area of sheet at 100°C, A₁₀₀ = 320.1 cm²

Rise in temperature, $\sf{\Delta{T}}$ = 100 – 0 = 100°C

Increase in surface area, $\sf{\Delta{A}}$ = A₁₀₀ – A₀ = 320.1 – 320 = 0.1 cm²

Coefficient of surface expansion ${\beta}$ is given by;

$\sf{\beta=\dfrac{\Delta{A}}{A_0\times\Delta{T}}}=\dfrac{0.1}{320\times100}\\\\\sf{=31\times{10}^{-7}/\degree{C}}$

∴ Coefficient of linear expansion;

$\sf{\alpha=\dfrac{\beta}{2}=\dfrac{31\times{10}^{-7} }{2}=15.5\times{10}^{-7}/\degree{C}}$

Hence, option A is correct.