2 Marks Questions

Question 12 Marks

What is the Young’s modulus for a perfect rigid body?

Answer

According to Hooke’s law,$\text{(Y)}=\frac{\text{stress}}{\text{longitudinal strain}}=\frac{\text{F}}{\text{A}}\times\frac{\text{l}}{\Delta\text{l}}$
For a perfectly rigid body, change in length $\Delta\text{l}=0,$ therefore longitudinal strain in zero.$\therefore\ \text{Y}=\frac{\text{F}}{\text{A}}\times\frac{\text{l}}{0}=\infty$
Hence, Young's modulus for a perfectly rigid body is infinite $(\infty)$

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Question 22 Marks

The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Answer

$\text{Y}=\frac{\text{stress}}{\text{strain}}$ As per question longitudinal strain for rubber and steel are equal.$\therefore\text{Y}\propto\text{stress}$
$\therefore\frac{\text{Y}_\text{steel}}{\text{Y}_\text{Rubber}}=\frac{\text{(stress})_\text{steel}}{\text{(stress})_\text{Rubber}}\text{ As the Y}_\text{steel}>\text{Y}_\text{Rubber}$
$\therefore\frac{\text{Y}_\text{steel}}{\text{Y}_\text{Rubber}}>1$
$\therefore\text{(stress})_\text{steel}$ is larger than $\text{(stress})_\text{Rubber}$

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Question 32 Marks

Is stress a vector quantity?

Answer

$\text{stress}=\frac{\text{Mognitude of restoring force by solid}}{\text{Area of cross - section}}$as deforming and restoring force are equal and opposite so no net direction is involved.
Hence, the stress is not a vector quantity just like pressure.

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Question 42 Marks

What is the Bulk modulus for a perfect rigid body?

Answer

Bulk Modulus $=\frac{-\text{p(V)}}{\Delta\text{V}}$ as the perfect rigid body does not change it's shape even at infinite (deforming a stretching) force. Hence, $\Delta\text{V}=0$$\Rightarrow\ \text{B}=\frac{\text{pV}}{\Delta\text{V}}=\frac{\text{pV}}{0}=\propto$
So the bulk modulus is infinity.

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