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Q6.1-3PE

Expert-verifiedFound in: Page 221

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**An automobile with 0.260** **m radius tires travels** **80,000** **km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?**

The answer is $5\times {10}^{7}$ revolutions.

- The radius of each of the tires is 0.260 m.
- The distance traveled is 80,000 km.

**The distance covered in one revolution of the tires will be their circumference, i.e., ${\mathbf{2}}{\mathit{\pi}}{\mathit{r}}$.**

Putting the value in the expression, we get :

$\begin{array}{c}d=\text{2}\times \text{(3.14)}\times \text{(0.260)}\\ d=\text{1.6328 \hspace{0.33em}m}\end{array}$

$\begin{array}{c}n=\frac{(80,000\text{\hspace{0.33em}}\mathrm{km})\times \left(\frac{1000\mathrm{m}}{1\mathrm{km}}\right)}{1.6328\text{\hspace{0.33em}}\mathrm{m}}\\ =4.9\times {10}^{7}\\ \approx 5\times {10}^{7}\text{\hspace{0.33em}}\mathrm{revolutions}\end{array}$

Hence, the automobile’s tires complete about $5\times {10}^{7}\text{\hspace{0.33em}}\mathrm{revolutions}$ to travel the total distance of 80,000 km.

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