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Standard XII

Physics

Thermal Expansion

A wire of len...

Question

A wire of length $2 m$ is made from $10 c m^{3}$ of copper. A force $F$ is applied so that its length increases by $2 n m$ . Another wire of length $8 m$ is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by

0.8 c m

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1.6 c m

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2.4 c m

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3.2 c m

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Solution

The correct option is D $3.2 c m$
$l = \frac{F L}{A Y} = \frac{F L^{2}}{(A L) Y} = \frac{F L^{2}}{V Y}$
$∴ l α L^{2}$ if volume of the wire remains constant
$\frac{l_{2}}{l_{1}} = (\frac{L_{2}}{L_{1}})^{2} = (\frac{8}{2})^{2} = 16$
$∴ l_{2} = 16 \times l_{1} = 16 \times 2 = 32 m m = 3.2 c m$

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A wire of length 2 m is made from 10 cm3 of copper. A force F is applied so that its length increases by 2 nm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by

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A wire of length $2 m$ is made from $10 c m^{3}$ of copper. A force $F$ is applied so that its length increases by $2 n m$ . Another wire of length $8 m$ is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by

The correct option is D $3.2 c m$
$l = \frac{F L}{A Y} = \frac{F L^{2}}{(A L) Y} = \frac{F L^{2}}{V Y}$
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$∴ l_{2} = 16 \times l_{1} = 16 \times 2 = 32 m m = 3.2 c m$