At 0^ ^ ^ C , a circular hole of diameter 2.00 cm is made in an aluminium plate. Determine its diameter at 100^ ^ ^ C . Given α for aluminium = 2.3 × 10^ -5 ^ ^ ^ ^ -1 .

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Quantrex Academy · Accepted Answer

Correct answer: B. 2.0046 cm

The expansion of a hole in a solid is identical to the expansion of the solid material itself.

The diameter of the hole at temperature

T

is given by the formula for linear expansion:

D_T = D_0 (1 + \alpha \Delta T)

Given:

D_0 = 2.00 \text{ cm}

\alpha = 2.3 \times 10^{-5} ^{}^{{}^{\circ}}\textC^{-1}

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

Substituting the values:

D_{100} = 2.00 [1 + (2.3 \times 10^{-5}) \times 100]

D_{100} = 2.00 [1 + 0.0023]

D_{100} = 2.00 \times 1.0023 = 2.0046 \text{ cm}

At 0^ ^ ^ C , a circular hole of diameter 2.00 cm is made in an...

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