A sheet of steel is 40 cm long and 5 cm broad at 0^{} C. The surface area of the sheet increases by 1.4 {~cm}² at 100^{} C. Coefficient of linear expansion of steel is

Correct Answer is : 3.5×10−5/∘C3.5 × 10^{-5} /{ }^{} C3.5×10−5/∘C

A sheet of steel is 40 cm long and 5 cm broad at 0^{} C. The surface area of the sheet increases by 1.4 {~cm}² at 100^{} C. Coefficient of linear expansion of steel is

Correct Answer is : 3.5×10−5/∘C3.5 × 10^{-5} /{ }^{} C3.5×10−5/∘C

Test Index

MHTCET 15 May 2024 Shift 1 Paper

Question : 42 of 150

Marks: +1, -0

A sheet of steel is 40 cm long and 5 cm broad at

0^{\circ} C

. The surface area of the sheet increases by

1.4 \mathrm{~cm}^{2}

100^{\circ} C

. Coefficient of linear expansion of steel is

$1.9 \times 10^{-5} /{ }^{\circ} C$
$2.4 \times 10^{-5} /{ }^{\circ} C$
$3.5 \times 10^{-5} /{ }^{\circ} C$
$7 \times 10^{-5} / C$

Validate

Solution:

Concept:

When a solid sheet is heated, its surface area increases. The coefficient of superficial expansion is twice the coefficient of linear expansion, giving

\Delta A = A_0 (2\alpha)\Delta T

Explanation:

First, compute the original area of the rectangular steel sheet:

A_0 = 40 \text{ cm} \times 5 \text{ cm} = 200 \text{ cm}^2

The given increase in surface area is

\Delta A = 1.4 \text{ cm}^2

The temperature change is

\Delta T = 100^\circ\text{C} - 0^\circ\text{C} = 100^\circ\text{C}

Substitute these values into the formula:

1.4 = 200 \times 2\alpha \times 100

This simplifies to

1.4 = 40000\alpha

Solving for the linear expansion coefficient,

\alpha = \frac{1.4}{40000}

This gives

\alpha = 0.000035 /^\circ\text{C} = 3.5 \times 10^{-5} /^\circ\text{C}

Answer:

The coefficient of linear expansion of steel is

3.5 \times 10^{-5} /^\circ\text{C}

, which matches option C.

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