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18 Nov 2021, 01:37
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If we consider that rpm & rps are speeds and that speed is proportional to distance, this is a simple speed-distance problem.
One revolution of the smaller rim is 28 Pi and One revolution of the larger rim is 35 Pi. Here the ratio is 4/5. But The smaller rim must have covered bigger distance than the bigger rim at the same amount of time. Therefore the distance ratio is 5/4.
Speed of the smaller rim is X rps or 60X rpm and travels the distance 5. The bigger rim travels the distance 4, what is the speed ?
When Time is constant (1 min 0r 60 sec in this case), Speed is proportional to distance. So, the speed of the larger rim is (60X / 5) * 4.
So, the answer is 48X.
One revolution of the smaller rim is 28 Pi and One revolution of the larger rim is 35 Pi. Here the ratio is 4/5. But The smaller rim must have covered bigger distance than the bigger rim at the same amount of time. Therefore the distance ratio is 5/4.
Speed of the smaller rim is X rps or 60X rpm and travels the distance 5. The bigger rim travels the distance 4, what is the speed ?
When Time is constant (1 min 0r 60 sec in this case), Speed is proportional to distance. So, the speed of the larger rim is (60X / 5) * 4.
So, the answer is 48X.
18 Nov 2021, 02:45
Kudos
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puma
This is similar to interlocked wheels. They both cover the same distance per second. So number of revolutions they make in a unit of time will depend on their circumference. More the circumference, fewer the revolutions. This means radius/diameter is inversely related to number of revolutions.
Their diameter is in the ratio 4:5 so their number of revolutions will be in the ratio 5:4. If the smaller rim makes x revolutions in a 1 sec, the bigger rim will make 4x/5 revolutions in 1 sec.
In 1 min, the bigger rim will make 60*4x/5 = 48x revolutions.
Answer (C)
04 Jun 2023, 02:41
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To determine the number of revolutions per minute the larger rim makes in terms of x, we need to compare the linear speeds of the two rims.
The linear speed of a rotating object can be calculated by multiplying the circumference of the circle by the number of revolutions per second.
For the smaller rim with a diameter of 28 inches, the circumference is π * 28 = 28π inches.
For the larger rim with a diameter of 35 inches, the circumference is π * 35 = 35π inches.
Both rims rotate the same number of inches per second, so we can set up the following equation:
28π * x = 35π * N,
where N represents the number of revolutions per minute for the larger rim.
To find N in terms of x, we divide both sides of the equation by 28π:
x = (35π * N) / (28π).
Simplifying, we get:
x = (5/4) * N.
To express the number of revolutions per minute, we convert x revolutions per second to (x * 60) revolutions per minute:
(x * 60) = (5/4) * N.
Simplifying further, we have:
N = (4/5) * (x * 60) = 48x.
Therefore, the larger rim makes (C) 48x revolutions per minute in terms of x.
The linear speed of a rotating object can be calculated by multiplying the circumference of the circle by the number of revolutions per second.
For the smaller rim with a diameter of 28 inches, the circumference is π * 28 = 28π inches.
For the larger rim with a diameter of 35 inches, the circumference is π * 35 = 35π inches.
Both rims rotate the same number of inches per second, so we can set up the following equation:
28π * x = 35π * N,
where N represents the number of revolutions per minute for the larger rim.
To find N in terms of x, we divide both sides of the equation by 28π:
x = (35π * N) / (28π).
Simplifying, we get:
x = (5/4) * N.
To express the number of revolutions per minute, we convert x revolutions per second to (x * 60) revolutions per minute:
(x * 60) = (5/4) * N.
Simplifying further, we have:
N = (4/5) * (x * 60) = 48x.
Therefore, the larger rim makes (C) 48x revolutions per minute in terms of x.
