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# What is the number of 360-degree rotations that a bicycle

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What is the number of 360-degree rotations that a bicycle [#permalink]

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23 Aug 2007, 15:42
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76% (01:37) correct 24% (00:37) wrong based on 196 sessions

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What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-number-of-360-degree-rotations-that-a-bicycle-wh-166668.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 May 2014, 01:55, edited 2 times in total.
Renamed the topic, edited the question and added OA.
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29 Sep 2011, 03:53
Statement 2: You can not simply use unitary method here. We don't know how much distance the wheel covers in one rotation. For example, say wheel covers 10m in one rotation, so it will take 10 rotations to cover 100m where as if wheel covers 5m in one rotation, it will will take 20 rotations to cover the same distance. Also number of rotation here is not a function of time taken to complete the rotation.
Hope it helps.
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29 Sep 2011, 06:49
siddhans wrote:
20 X 60 (secs) = 1200 m travelled

How does number 20 multiplied by 60 seconds became 1200 meters ?
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01 Oct 2011, 02:08
siddhans wrote:
Searched but couldnt find... so posted

what is the number of 360 degree rotations that a bicycle wheel made while rotating 100 meters in a straight line without slipping?

1) The diameter of the bicycle wheel , including the tire, was 0.5 m

2) The wheel made twenty 360-degree rotations per min

[Reveal] Spoiler: My doubt
1) No of rotations = Total Distance/ Circumference = 100/2 * pi *r
1 --- Sufficient

2) 20 rotations in 60 secs

Rate X Time = Distance travelled

20 X 60 (secs) = 1200 m travelled

It travels 1200 m in 60 secs

1200 m ----- 60 secs
100 m -----??

cross - multiply

100 *60
--------- = 5 secs
1200

Rate * time = distance

Plug in distance =100 m

time = 5 secs

rate = 20

So ans should be D

but OA is A

What am i doing wrong here?

(1) n x pi x diameter = distance moved
distance moved = 100m
diameter = 0.5m
n = number of rotations

n = 100/(pi x 0.5)
Sufficient

(2) Not sufficient to get "n"

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Re: What is the number of 360 degree rotations that a bicycle [#permalink]

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06 Jan 2013, 04:55
How do you solve this one?
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Re: What is the number of 360 degree rotations that a bicycle [#permalink]

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06 Jan 2013, 05:24
Expert's post
fozzzy wrote:
How do you solve this one?

The distance is given. The question is asking the number of 360 degree rotations.
By 360 degree rotations, it means the number of revolutions.
The number of revolutions don't depend on the speed but just the radius.
The number of revolutions will be $$1000/2*pi*R$$.

Statement 2 just gives the speed, but it doesn't gives the radius.
Hence +1A
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Re: What is the number of 360 degree rotations that a bicycle [#permalink]

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07 Jan 2013, 06:37
Marcab wrote:
fozzzy wrote:
How do you solve this one?

The distance is given. The question is asking the number of 360 degree rotations.
By 360 degree rotations, it means the number of revolutions.
The number of revolutions don't depend on the speed but just the radius.
The number of revolutions will be $$1000/2*pi*R$$.

Statement 2 just gives the speed, but it doesn't gives the radius.
Hence +1A

Is this the general formula to solve this type of problems so I can apply this to PS questions
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Re: What is the number of 360-degree rotations that a bicycle [#permalink]

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07 Jan 2013, 06:41
Expert's post
No its not a formula. Its simple logic.
Circumfrence is the total distance that a wheel will cover in one rotation. Since the distance is 1000m, therefore the number of revolutions will be 1000/circumfrence.
Hope its clear.
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14 Nov 2013, 08:13
Let me put it this way
Distance (m) = Speed (m/s) * Time (s) => (m/s)*s = metres
In the explanation that you had put forward, you had used "no of rotations" in place of speed. No of rotations is basically a number. It does not translate into speed.
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Re: What is the number of 360-degree rotations that a bicycle [#permalink]

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21 May 2014, 01:16
Sumithra Sen wrote:
What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

I see how this must be A. But how can you consider the tire to be of negligible thickness when it does not say so in statement 1? Moreover the question does not say anything about the tire. Don't you need to consider its thickness? In which case, it will be E.

Can someone explain this?
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Re: What is the number of 360-degree rotations that a bicycle [#permalink]

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21 May 2014, 01:59
Expert's post
1
This post was
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petrifiedbutstanding wrote:
Sumithra Sen wrote:
What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

I see how this must be A. But how can you consider the tire to be of negligible thickness when it does not say so in statement 1? Moreover the question does not say anything about the tire. Don't you need to consider its thickness? In which case, it will be E.

Can someone explain this?

(1) says that "the diameter of the bicycle wheel, including the tire, was 0.5 meter". So, we have the diameter of the whole wheel, we don't need the the thickness of tire.

What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

1 revolution of a circle = circumference of that circle. So, we basically asked to find the value of 100/(circumference).

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter. We can get the circumference. Sufficient.

(2) The wheel made twenty 360-degree rotations per minute. We cannot get the circumference. Not sufficient.

Similar questions to practice:
a-circular-rim-28-inches-in-diameter-rotates-the-same-number-65106.html
two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html
how-long-in-minutes-did-it-take-a-bicycle-wheel-to-roll-130026.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-number-of-360-degree-rotations-that-a-bicycle-wh-166668.html
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Re: What is the number of 360-degree rotations that a bicycle [#permalink]

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21 May 2014, 02:12
Expert's post
petrifiedbutstanding wrote:
Sumithra Sen wrote:
What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

I see how this must be A. But how can you consider the tire to be of negligible thickness when it does not say so in statement 1? Moreover the question does not say anything about the tire. Don't you need to consider its thickness? In which case, it will be E.

Can someone explain this?

Responding to a pm:

Whatever is the number of rotations made by the outside surface of the wheel, the same will be the number of rotations made by the entire wheel. Imagine inserting a long needle from the tire reaching up to the center of the wheel. Every point in the needle will complete one circle at the same time.

Also, the stmnt tells you that the diameter of the wheel including the tire is 0.5 to clarify properly. Else, in common parlance, wheel pretty much includes the tire as well.
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