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Question
When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
Options
\[\frac{∆ \text{l}}{\text{ l }}\]
\[\left( \frac{∆ \text{ l }}{\text{ l }} \right)^2\]
\[\sqrt{∆ \text{ l / l}}\]
none of these
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Solution
\[\frac{∆ \text{l}}{\text{ l }}\]
\[\text{ C . S . A . = A }\]
\[\text{ Length = l}\]
\[\text{ Volume of the wire V = Al }\]
\[\text{ Assuming no lateral strain when longitudinal strain occurs: }\]
\[\text{ Increase in volume: ∆ V = A ∆ l }\]
\[ \Rightarrow \frac{∆ V}{V} = \frac{A ∆ \text{ l }}{\text{ Al }} = \frac{∆ \text{ l }}{\text{ l }}\]
\[\text{ So,} \frac{∆ V}{V} \text{ is directly proportional to } \frac{∆ \text{l}}{\text{ l }}\] .
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