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Some Mechanical Properties of Matter — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSome Mechanical Properties of Matter1 Mark
MCQ
When a metal wire is stretched by a load, the fractional change in its volume $\frac{\triangle\text{V}}{\text{V}}$ is proportional to.
  • ✓
    $\frac{\triangle\text{l}}{\text{l}}$
  • B
    $\Big(\frac{\triangle\text{l}}{\text{l}}\Big)^2$
  • C
    $\sqrt{\frac{\triangle\text{l}}{\text{l}}}$
  • D
    None of these.
✓

Answer

Correct option: A.
$\frac{\triangle\text{l}}{\text{l}}$
C.S.A = A
Lenghth = l
Volume of the wire V = Al
Assuming no lateral strain when longitudinal strain occurs:
Increase in volume: $\triangle\text{V}=\text{A}\triangle\text{l}$
$\Rightarrow\frac{\triangle\text{v}}{\text{V}}=\frac{\text{A}\triangle\text{l}}{\text{A}\text{l}}=\frac{\triangle\text{l}}{\text{l}}$
So, $\frac{\triangle\text{V}}{\text{V}}$ is directly proportional $\frac{\triangle\text{l}}{\text{l}}\cdot$

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