MCQ
A rectangular block is heated from $0^{\circ} C$ to $100^{\circ} C$. The percentage increase in its length is $0.10 \%$. What will be the percentage increase in its volume?
- A$0.03 \%$
- B$0.10 \%$
- C$0.30 \%$
- D$0.50 \%$
✓
Answer
C. $0.30 \%$
Explanation:
As $\frac{\Delta L}{L}=0.10 \%=0.001$ and $\Delta T=100^{\circ} C$, hence using $\frac{\Delta L}{L}= a \Delta T$,
we get; $a =\frac{0.001}{100}=\frac{10^{-5}}{{ }^{\circ} C }$
$\therefore \gamma=3 \alpha=\frac{3 \times 10^{-5}}{{ }^{\circ} C }$
and $\frac{\Delta V}{V}=\gamma \Delta T=3 \times 10^{-5} \times 100=3 \times 10^{-3}=0.30 \%$
Explanation:
As $\frac{\Delta L}{L}=0.10 \%=0.001$ and $\Delta T=100^{\circ} C$, hence using $\frac{\Delta L}{L}= a \Delta T$,
we get; $a =\frac{0.001}{100}=\frac{10^{-5}}{{ }^{\circ} C }$
$\therefore \gamma=3 \alpha=\frac{3 \times 10^{-5}}{{ }^{\circ} C }$
and $\frac{\Delta V}{V}=\gamma \Delta T=3 \times 10^{-5} \times 100=3 \times 10^{-3}=0.30 \%$
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