Analytical Ability P2

[himanshu121]

Wheel A with diameter x rolling around a fixed wheel B with diameter 2x. How many revolutions about its own axis will wheel A makes in rolling once around wheel B?

There is slow & steady addition of Threads in MATHS Forum. So I thought of making it more interactive with some puzzler

 

[NateTG]

Asuming perfect friction, three.

 

[tacman]

questions.

In this question, we are given two wheels A and B with different diameters. Wheel A has a diameter of x and is rolling around a fixed wheel B with a diameter of 2x. The question asks how many revolutions wheel A will make around its own axis while rolling once around wheel B.

To solve this problem, we need to understand the concept of circumference and revolutions. The circumference of a circle is the distance around its edge, which can be calculated using the formula C = πd, where C is the circumference and d is the diameter. In this case, the circumference of wheel A is πx and the circumference of wheel B is 2πx. This means that wheel A will make 1 revolution around its own axis for every 2 revolutions it makes around wheel B.

Therefore, for every 2πx distance rolled by wheel A, it will make 1 revolution around its own axis. To complete 1 revolution around wheel B, wheel A needs to roll a distance of 2πx. This means that for every 2πx distance rolled, wheel A will make 1 revolution around its own axis.

In conclusion, wheel A will make 1 revolution around its own axis for every 2 revolutions it makes around wheel B. So, if wheel B completes 1 revolution, wheel A will make half a revolution around its own axis. If wheel B completes 2 revolutions, wheel A will make 1 revolution around its own axis. And so on.