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The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr?
Given:
The wheel of a motor cycle is of radius $35\ cm$.
Speed of the motor cycle is $66\ km/h$.
To do:
We have to find the number of revolutions per minute.
Solution:
The radius of a wheel $=r=35\ cm$
$=0.35\ m$
The speed it must keep $=s=66\ km/h$
$=\frac{66\times1000}{60}\ m/min$
$=1100\ m/min$
Let the number of revolutions it makes per minute to maintain that speed $=n$.
The circumference of the wheel $C=2\pi r$
$=2\times \frac{22}{7}\times0.35\ m$
$=2.2\ m$
The distance the wheel covers in $1\ min=1100\ m$
The distance covered by the wheel in one revolution$=$ The circumference of the wheel
Here,
The number of revolution$=n=\frac{Distance\ covered( d)}{Circumference\ of\ the\ wheel( C)}$
$=\frac{1100}{2.2}$
$=500$
The number of revolutions per minute is $500$.
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