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Standard XII

Physics

Thermal Expansion

A wire of len...

Question

A wire of length 2m is made from $10 c m^{3}$ of copper. A force F is applied so that its length increases by 2 mm. 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 cm

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1.6 cm

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2.4 cm

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3.2 cm

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Solution

The correct option is D 3.2 cm
$l = \frac{F L}{A Y} = \frac{F L^{2}}{V Y}$ $∴ l \propto L^{2}$ [As V, Y and F are constant]
$\frac{l_{2}}{l_{1}} = {[\frac{L_{2}}{L_{1}}]}^{2} = {(\frac{8}{2})}^{2} = 16 \Rightarrow l_{2} = 16 l_{1} = 16 \times 2 m m = 32 m m = 3.2 c m$

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A wire of length 2m is made from 10cm3of copper. A force F is applied so that its length increases by 2 mm. 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 cml=FLAY=FL2VY ∴l∝L2 [As V, Y and F are constant] l2l1=[L2L1]2=(82)2=16⇒l2=16l1=16×2mm=32 mm=3.2 cm

A wire of length 2m is made from $10 c m^{3}$ of copper. A force F is applied so that its length increases by 2 mm. 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 cm
$l = \frac{F L}{A Y} = \frac{F L^{2}}{V Y}$ $∴ l \propto L^{2}$ [As V, Y and F are constant]
$\frac{l_{2}}{l_{1}} = {[\frac{L_{2}}{L_{1}}]}^{2} = {(\frac{8}{2})}^{2} = 16 \Rightarrow l_{2} = 16 l_{1} = 16 \times 2 m m = 32 m m = 3.2 c m$