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A tire on a car rotates at 500 RPM (revolutions per minute) when the car is traveling at 50 km/hr. What is the circumference of the tire, in m?

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\frac{10 π}{6}

\frac{50, 000}{60 * 2 π}

\frac{50, 000}{500 * 2 π}

\frac{10}{6}

answer is D.

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Detailed Solution

We have been given,
A tire on a car rotates at 500 RPM (revolutions per minute) when the car is traveling at 50 km/hr.
Speed

= \frac{50 km}{hr}

= \frac{50, 000 m}{hr}

Speed

(\frac{in m}{\min}) = \frac{\frac{50, 000}{60 m}}{\min}

Thus,
Per minute the car travels

\frac{\frac{50, 000}{60 m}}{\min}

tire volutes

500

times around or

500

times its circumference.
Calculating the circumference,
Let the circumference be C.

\Rightarrow \frac{50, 000}{60} = 500 C

C = \frac{50, 000}{500 \times 60}

C = \frac{10}{6} m

Therefore, the circumference is

\frac{10}{6}

m.
Hence, option 4 is correct.

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