Sure, let's solve this problem step by step.
1. Given Data:
- Initial diameter of the coin, [tex]\( D_0 = 1.5000 \)[/tex] meters.
- Coefficient of linear expansion, [tex]\( \alpha = 2 \times 10^{-5} \, \text{°C}^{-1} \)[/tex].
- Temperature change, [tex]\( \Delta T = 1 \, \text{°C} \)[/tex] (Assumed).
2. Calculate the change in diameter ([tex]\( \Delta D \)[/tex]):
The formula to determine the change in diameter due to thermal expansion is:
[tex]\[
\Delta D = D_0 \times \alpha \times \Delta T
\][/tex]
Plugging in the values:
[tex]\[
\Delta D = 1.5000 \times 2 \times 10^{-5} \times 1
\][/tex]
3. Determine the change in diameter ([tex]\( \Delta D \)[/tex]):
The calculation yields:
[tex]\[
\Delta D \approx 0.0000 \, \text{meters}
\][/tex]
4. Calculate the new diameter ([tex]\( D \)[/tex]):
The new diameter is the initial diameter plus the change in diameter:
[tex]\[
D = D_0 + \Delta D
\][/tex]
Given that:
[tex]\[
D = 1.5000 + 0.0000
\][/tex]
[tex]\[
D \approx 1.5000 \, \text{meters}
\][/tex]
5. Final Answer:
The diameter of the Nepali two rupee coin on a hot day will be approximately [tex]\( 1.5000 \)[/tex] meters, accurate to four decimal places.
