Problem Solving

A wheel of a car of radius 21 cms is rotating at 600 rotations per minute. What is the speed of the car in km/hr?

A. 79.2 km/hr
B. 47.52 km/hr
C. 39.6 km/hr
D. 7.92 km/hr
E. 3.96 km/hr

The OA is B.

Can any expert help me with this PS question please? I don't understand it.

A wheel of a car of radius 21 cms is rotating at 600 rotations per minute. What is the speed of the car in km/hr?

A. 79.2 km/hr
B. 47.52 km/hr
C. 39.6 km/hr
D. 7.92 km/hr
E. 3.96 km/hr

The OA is B.

Can any expert help me with this PS question please? I don't understand it.

Hi LUANDATO,
Let's take a look at your question.

We can see that the radius of the wheel is given in cm. We will first convert it to km because we need to find the speed of the car in km/h. Therefore,
Radius = 21 cm = 21/100 m = 0.21m
Now convert m to km by dividing 0.21 by 1000,
Radius = 0.21/1000 = 0.00021 km

We will now find the circumference of the wheel to find out how much distance the wheel will cover in one rotation.
$$Circumference=2\pi r$$
$$Circumference=2\times\frac{22}{7}\times0.00021$$
$$Circumference=0.00132\ km$$

So One rotation = 0.00132 km
In one minute the wheel is taking 600 rotations per minute.

The distance covered in 600 rotations = 600 x Distance covered in one rotation
$$=0.00132\ \times600\ $$
$$=0.792\ km$$

In one minute the distance covered = 0.792 km
In 60 minutes the distance covered = 0.792 x 60 = 47.52 km

It means the speed of the car is 47.52 km per hour.
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.