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8. mechanical properties of solids — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics8. mechanical properties of solids1 Mark
MCQ
The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume $?$ The volume elasticity of the cube is $\beta $ and the coefficient of volume expansion is $\alpha $
  • ✓
    $\frac{P}{{\alpha \beta }}$
  • B
    $\frac{{P\alpha }}{\beta }$
  • C
    $\frac{{P\beta }}{\alpha }$
  • D
    $\frac{{\alpha \beta }}{P}$
✓

Answer

Correct option: A.
$\frac{P}{{\alpha \beta }}$
a
(a) If coefficient of volume expansion is $\alpha $ and rise in temperature is $\Delta \theta $ then $\Delta V = V\alpha \Delta \theta $$\Rightarrow $ $\frac{{\Delta V}}{V} = \alpha \Delta \theta $

Volume elasticity $\beta = \frac{P}{{\Delta V/V}}$ $ = \frac{P}{{\alpha \Delta \theta }}$==> $\Delta \theta = \frac{P}{{\alpha \beta }}$

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