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1.Units, Dimensions and Measurement
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The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly
A
$0.15 \%$
B
$0.30 \%$
C
$0.60 \%$
D
$0.0225 \%$
(KVPY-2009)
Solution
(b)
Percentage increase in area
$=\frac {Final \,area – Initial \,area}{Initial \,area} \times 100$
$=\frac{\pi\left(r_2^2-r_1^2\right)}{\pi r_1^2} \times 100$
$=\frac{\left(r_1+\Delta r\right)^2-r_1^2}{r_1^2} \times 100$
where, $\Delta r=$ increase in radius.
$=\left(\frac{r_1^2+2 r_1 \Delta r+\Delta r^2-r_1^2}{r_1^2}\right) \times 100$
$=\frac{2 r_1 \Delta r+\Delta r^2}{r_1^2} \times 100$
As $\Delta r$ is small, we can neglect $\Delta r^2$.
$\approx \frac{2 r_1 \Delta r}{r_1^2}=100$
$=2(\frac{\Delta r}{r_1} \times 100)$
$=2 \times 0.15 \%=0.30 \%$
Standard 11
Physics
