There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls 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 ?
[amp_mcq option1=”31 cm” option2=”32 cm” option3=”33 cm” option4=”34 cm” correct=”option3″]
Radius of the larger circle (R2) = 110 m = 11000 cm.
Radius of the first wheel (r1) = 30 cm.
Let N be the number of revolutions made by each wheel on its axis.
The first wheel rolls on the smaller circle (R1). The distance covered by its point of contact is the circumference of the smaller circle, which is 2πR1. This distance is also equal to N times the circumference of the first wheel, which is N * 2πr1.
So, 2πR1 = N * 2πr1
R1 = N * r1
10000 = N * 30
N = 10000 / 30 = 1000 / 3
The second wheel rolls on the larger circle (R2). Let its radius be r2. The distance covered by its point of contact is the circumference of the larger circle, which is 2πR2. This distance is also equal to N times the circumference of the second wheel, which is N * 2πr2.
So, 2πR2 = N * 2πr2
R2 = N * r2
We know R2 = 11000 cm and N = 1000/3.
11000 = (1000/3) * r2
r2 = 11000 * (3 / 1000)
r2 = 11 * 3 = 33 cm.
The radius of the other wheel is 33 cm.