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A circular rim 28 inches in diameter rotates the same number

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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 26 Mar 2015, 09:23
Hey guys, A simple application of kinematics.

V1= linear velocity of the rim of small diameter.

V2= linear velocity of the rim of large diameter.

r1 =radius of smaller rim, i.e. (28/2= 14 in)

r2= radius of larger rim, i.e. (35/2 =17.5 in)

w1=2*pi*f1= angular velocity(w1) and frequency(f1) of rotation of smaller rim.

W2=2*pi*f2= angular velocity(w2) and frequency(f2) of larger rim.

Acc. to the query v1=v2 which implies,

or, 2*pi*r1*f1 = 2*pi*r2*f2

or, 2*22/7*14*f1 = 2*22/7*17.5*f2

or, 88f1=110f2

or, f2= (4/5)f1

but, revolution per MINUTE is being asked, then

or, f2=(4/5)*60*f1

therefore, f2 = 48f1.

Thus option C is opted thus.

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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 02 May 2016, 09:30
puma wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75


Here is an alternate time saving solution with the use of ratios.
Now the ratio of the rims circumferences will be same as the ratio of their radii.(find out why :) ) Now R/r=35/28=5/4.
Then the ratio of their speeds will be opposite to their ratio of time and ratio of the time taken = ratio of their radii if we keep distance constant. So we know that larger circle will have a lower revolution speed than smaller.
Now a,e,b are out. Left only c and d.
Now we know revolution = x per sec. So 60x/min. So larger rim rev=60x*(inversed ratio)= 60x*4/5= 48x
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 22 Jul 2016, 23:28
puma wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75


One rotation of the wheel is equal to its circumference = pi*diameter

Total distance covered in t time will be = pi*d*rate of revolution *time taken

Now the distance covered is equal for both the wheels, in 1second therefore -
28pi*x*1sec=35pi*R*1sec
28x=35R
R=28x/35
This is the rate for bigger 35 inch wheel per second
In one minute the bigger will cover Rate *time (60 seconds) = (28x/35) *60 ---> 48x

ANSWER IS C
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A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 26 May 2017, 11:32
puma wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75


Okay..here it goes..

Lets call the smaller one A and the larger one B.

A's diameter = \(28\), so circumference = \(28\pi\)
B's diameter = \(35\), so circumference = \(35\pi\)

Let the number of revolutions of A = x, and those of B = y.
According to the question..
\(28\pi*x = 35\pi*y\)

Thus,


\(y = \frac{4}{5}x\)

But that's the value of revolutions per second. For per minute..multiply it with 60.

Answer 48x(C).
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 29 May 2017, 00:51
puma wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1. We will convert x revolutions per second of the smaller rim as 60x revolutions per minute
2. The distance rotated per second is the same for both but since the diameters are different, we know that the larger rim makes lesser revolutions per second
3. The ratio of the number of revolutions of the two rims are given by the inverse of the ratio of their diameters.
4. So the number of revolutions per minute of the larger rim is 60x *(28/35) = 48x.
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Re: A circular rim 28 inches in diameter rotates the same number  [#permalink]

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New post 30 Jan 2018, 11:27
puma wrote:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75


The smaller rim rotates at a rate of 28πx inches per second. Since the larger rim rotates the same number of inches per second, it rotates at a rate of 28πx inches per second also, and, in one minute, it rotates 28πx * 60 inches.

Since 1 rotation of the larger rim = its circumference = 35π, the number of rotations made by the larger rim will thus be:

(28πx * 60)/35π

(4x * 60)/ 5

4x * 12

48x

Answer: C
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Re: A circular rim 28 inches in diameter rotates the same number &nbs [#permalink] 30 Jan 2018, 11:27

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