The wheels of the locomotive of a train are 2.1 m in radius. They make 75 revolutions in one minute. Find the speed of the train in km per hour.

Given radius of wheel = R = 2.1m

Number of revolutions in one minute = 75

Number of revolutions in 1 hour = 75×60

Number of revolutions in 1 hour = 45000

Distance covered in one revolution = Circumference of wheel

Distance covered in 1 revolution = 2πR (where R = radius of wheel)

Distance covered n 1 revolution = 2π(2.1)

= 13.2 m

So, distance covered in 4500 revolutions = 4500×distance covered in 1

Distance covered in 4500 revolution = 4500× 13.2

Distance covered in 4500 revolutions = 59400 m = 59.4 km

∴ Distance covered in 1 hour = 59.4 km

Hence speed of the locomotive = 59.4 km/hr

The speed of locomotive is 59.4 km/hr