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28 Aug 2020, 07:36
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C
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Difficulty:
95%
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Question Stats:
13% (01:48) correct
87%
(01:43)
wrong
based on 86
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Circular disc, A rolls around another circular disc, B (without slipping). It starts at the top of the disc B and continues until it reaches its starting position. How many revolutions does disc A make in total around its center, if radius of disc B is 4 times that of disc A.
A. 3
B. 4
C. 5
D. 6
E. 8
A. 3
B. 4
C. 5
D. 6
E. 8
28 Aug 2020, 11:08
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A tricky question.
If the radius of A is x, then radius of B = 4x
Circumference of B = \(2\pi * 4x\) = \(8 \pi x\) is the distance that has to be traveled by the smaller circle of circumference \(2 \pi x\).
Therefore the number of revolutions should be \(\frac{8 \pi x}{2 \pi x} = 4\)
If this were a straight road instead of a circle, this answer would have been correct.
Since the disc is moving around the circle, there is a second movement happening with the revolution, which is a rotation.
One rotation of the smaller disc from the staring point to the end point is 1 extra revolution.
In general the total number of revolutions of a circular disc around another circle = n + 1, where n is the number of revolutions found by dividing the larger circumference by the smaller circumference the +1 accounts for the revolution due to the 1 rotation.
The Correct answer is Option C
Arun Kumar
If the radius of A is x, then radius of B = 4x
Circumference of B = \(2\pi * 4x\) = \(8 \pi x\) is the distance that has to be traveled by the smaller circle of circumference \(2 \pi x\).
Therefore the number of revolutions should be \(\frac{8 \pi x}{2 \pi x} = 4\)
If this were a straight road instead of a circle, this answer would have been correct.
Since the disc is moving around the circle, there is a second movement happening with the revolution, which is a rotation.
One rotation of the smaller disc from the staring point to the end point is 1 extra revolution.
In general the total number of revolutions of a circular disc around another circle = n + 1, where n is the number of revolutions found by dividing the larger circumference by the smaller circumference the +1 accounts for the revolution due to the 1 rotation.
The Correct answer is Option C
Arun Kumar
General Discussion
31 Aug 2020, 20:14
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hmmm, you got me. Tricky question. Still trying to picture this in my head. Googling now, but any extra insight would be helpful (I guess finding a picture would be the most help)
EDIT: https://plus.maths.org/content/circles-rolling-circles
Playing with my coins now.....gotta love the GMAT
EDIT: https://plus.maths.org/content/circles-rolling-circles
Playing with my coins now.....gotta love the GMAT
