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JAMB Physics 2019 Paper

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Question : 80

Total: 100

A copper rod, 5m long when heated through 10c, expands by 1mm. If a second copper rod, 2.5m long is heated through 5c, by how much will it expand?

4mm
0.25mm
2mm
0.12mm

Solution:

Concept:

Linear expansion is directly proportional to original length and temperature change for the same material.

Explanation:

Use

\Delta L = \alpha L \Delta T

.

Since both rods are copper,

\alpha

is the same, so compare the two cases:

\frac{\Delta L_2}{\Delta L_1} = \frac{L_2 \Delta T_2}{L_1 \Delta T_1}

.

Given:

L_1 = 5\text{m}

,

\Delta T_1 = 10^\circ\text{C}

,

\Delta L_1 = 1\text{mm}

.

Also:

L_2 = 2.5\text{m}

,

\Delta T_2 = 5^\circ\text{C}

.

Substitute:

\frac{\Delta L_2}{1\text{mm}} = \frac{2.5 \times 5}{5 \times 10}

.

Simplify:

\frac{12.5}{50} = 0.25

.

So

\Delta L_2 = 0.25 \times 1\text{mm} = 0.25\text{mm}

.

Answer:

0.25\text{mm}

, which is option B.

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