There are two concentric circles . The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm on the smaller circle and another wheel on the larger circle. After they have completed one revolution, it is found that the two whee

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Q: 52 (CAPF/2016)
There are two concentric circles . The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm on the smaller circle and another wheel on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times on their respective axes. What is the radius of the other wheel?

question_subject: 

Maths

question_exam: 

CAPF

stats: 

0,12,8,4,4,12,0

keywords: 

{'concentric circles': [0, 0, 0, 1], 'radius': [0, 0, 2, 2], 'circles': [0, 1, 0, 0], 'smaller circle': [0, 0, 0, 1], 'larger circle': [0, 0, 0, 1], 'wheel': [0, 0, 0, 1], 'other wheel': [0, 0, 0, 1], 'respective axes': [0, 0, 0, 1], 'wheels': [1, 0, 2, 1], 'equal number': [1, 0, 0, 5], 'revolution': [0, 0, 0, 1], 'radii': [0, 0, 0, 2]}

To solve this problem, we need to find the radius of the other wheel.

Let`s consider the wheel on the smaller circle first. The radius of the smaller circle is 100 m. The circumference of the circle is 2πr, where r is the radius. So, the circumference of the smaller circle is 2π(100) = 200π m.

Now, let`s consider the wheel on the larger circle. The radius of the larger circle is 110 m. The circumference of this circle is 2π(110) = 220π m.

We are given that after one revolution, both wheels rolled an equal number of times on their respective axes. This means that the distance traveled by both wheels is the same.

The distance traveled by the smaller wheel is equal to its circumference, which is 200π m.

The distance traveled by the larger wheel is equal to its circumference, which is 220π m.

Since both distances are equal, we can set up the following equation:

200π = 220π

Dividing both sides of the equation by π, we get:

200 = 220

From this equation, we can see that 200 is not equal to 220.

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