QUESTION

# Each wheel of a car is of diameter 80cm. How many complete revolutions does each wheel make in 10 min when the car is travelling at a speed of 66 km/hr[a] 4363[b] 4376[c] 4375[d] None of the above.

Hint: Calculate the distance covered in one revolution of the wheel. Hence calculate the total number of revolutions equivalent to 66kms. This will give the number of revolutions per hour. Hence calculate the number of revolutions in 10 mins. Alternatively, calculate the angular velocity of the wheel and hence the number of revolutions in 10mins.

The wheel covers a distance equal to the length of the circumference of the wheel in one revolution.
Given the diameter of the wheel = 80 cm =0.8 m
Hence the radius of the wheel = 0.4m.
Hence distance covered in one revolution $=2\pi \left( 0.4 \right)=0.8\pi$ .
Hence the number of revolutions in 1 hour $=\dfrac{66\times 1000}{0.8\pi }=\dfrac{66000\times 7}{0.8\times 22}=\dfrac{21000}{0.8}=26250$ revolutions.
Hence the number of revolutions in 60 mins = 26250
Hence the number of revolutions in 1 min $=\dfrac{26250}{60}=437.5$
Hence the number of revolutions in 10 mins $=437.5\times 10$ = 4375 revolutions.
Hence option [c] is correct.

Note: The speed at the circumference of the wheel = 66km/h $=\dfrac{66\times 1000}{60}\text{m/min=}$ 1100 m/min.
We know that angular velocity $=\dfrac{\text{Velocity at point P}}{\text{Distance of point P from centre}}$
Hence, we have
Angular velocity $=\dfrac{1100}{0.4}\text{rad}/\min =2750$ rad/min
Since in a complete revolution we cover $2\pi$ radians, we have
The number of revolutions in 1 min $=\dfrac{2750}{2\pi }=437.5$
Hence the number of revolutions in 10 mins = 4375 revolutions.
Hence option [c] is correct.