Question

The diameter of the wheel of a car is 56 cm. Calculate the speed of the car in kmph if it wheel makes 750 revolutions per minute

Answer 1

Hint: We will find the number of revolutions per hour first. Then 2πr x no. of revolutions will give the distance travelled per hour which is speed.

Complete step-by-step answer:
The number of revolutions per minute has the units of 1/s. The circumference, obviously, has units of metre. Hence the multiplication of them would have units of m/s. You can use this trick to find out possible expressions for a quantity given certain data, if you don’t know the exact formula for that quantity.
Firstly, 750 revolutions per minute
$ = 60 \times 750$ revolutions per hour $ = 45,000$ rev/hr.
$r = \dfrac{{56}}{2}{\rm{cm}} = \dfrac{{56}}{2} \times {10^{ - 5}}{\rm{km}} = 28 \times {10^{ - 5}}{\rm{km}}$
Speed in km/hr $ = 45,000$ rev/hr $ \times 2\pi \times \dfrac{{56}}{2} \times {10^{ - 5}}$ km
(Note that the conversion from m/s to km/h is the following: speed in m/s $ \times $ (18/5) = speed in km/h)
Taking $\pi = \dfrac{{22}}{7}$ ( this is an approximation that we take because the diameter is divisible by 7. Normally, do not make this approximation unless the question asks for it. In this case, since the radius is a multiple of 7, a round figure solution can be arrived at easily by taking $\pi = \dfrac{{22}}{7}$.)

Speed ${\rm{S}} = 45,000 \times 2 \times \dfrac{{22}}{7} \times 28 \times {10^{ - 5}}$
$S = 79.2\;\;km/h$

Note: Be very careful while converting units
x rev/min $ = 60x$rev/hr.
We can also directly use πd to calculate the circumference of the wheel instead of 2πr since d is already given to us.