Two interconnected, circular gears travel at the same circumferential

Question

Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

OptimusPrepJanielle · Accepted Answer

Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B

Time A = 2*pi*25/Speed A
Time B = 2*pi*15/Speed B

Since the times are same,

50pi/Speed A = 30pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/3

Correct Option: C

KarishmaB · Answer

Smaller the diameter, more the number of revolutions made since the circumferential rate of travel is the same for both gears (this just means that they cross the same distance in the given time). So smaller diameter means smaller circumference and hence more complete circles of travel. 
Circumference of A/Circumference of B = Number of revolutions of B/Number of revolutions of A

Number of revolutions of B/Number of revolutions of A  = 30\pi/50\pi

Number of revolutions of A/Number of revolutions of B = 5/3

Answer (C)

narmadadhruv · Answer

the bigger the diameter, the more distance wheel covers per revolutions  OR  lesser the revolutions wheel takes to cover the same distance. Going by this, rev. is inversely proportional to the diameter. Hence,  \frac{(rev. of A)}{(rev. of B)}  = \frac{(diameter of B)}{(diameter of A)} =\frac{3}{5}

rohit8865 · Answer

Distance covered by A=2*pi*r--------->30*pi
Distance covered by B=2*pi*r--------->50*pi
since their rates are equal
ratio=30*pi/50*pi==3/5
Ans A

gracie · Answer

A rpm*30⫪=B rpm*50⫪
A rpm/B rpm=50⫪/30⫪=5/3
answer c

tarunvns · Answer

it is given that rate is same i.e. the distance covered by A & B is same i.e.
Distance=circumference*revolution
so we can derive this relation

30*A=50*B (pie is canceled out)
A/B= 5/3

JeffTargetTestPrep · Answer

We see that Gear A has a circumference of 30π and Gear B has a circumference of 50π.

Since Gear A will make more revolutions than Gear B, the ratio is 50π/30π = 5/3.

Answer: C

nkmungila · Answer

The circumference of circle = 2*Pi*r
here 2*pi constant 
the number of revolution A should be more 
hence it should be 5:3
Answer C

Designated Target · Answer

Both gears travel at the same rate x centimeter/min
Gear A travel x centimeters = x/30 revolution per minute
Grear B travel x centimeters = x/50 revolutions per minute
=> Ratio = (x/30)/(x/50) = 5:3
Hope it clears

mm229966 · Answer

A = 30 cm;
B = 50 cm;
A/B = 3/5 => 5A = 3B

Answer: 5:3

Fdambro294 · Answer

Can get in and out in less than a minute if you understand the basic relationship between the 2 circular gears:

Distance Gear Travels per unit of time

= (# Revolutions per unit of time) * (Circumference)

If the distance each year travels is the same ——-> distance is Constant ———> then the ratio of the (# of revolutions per minute) is inversely proportional to the ratio of the two (circumference measures) of the gears

In fact, the ratio of diameters or radii can be used in place of the circumference.

(Diameter of A) : (Diameter of B) = 30 : 50 = 3 : 5

(No of Rev of A per unit of time) : (No of Rev of B per unit of time) = 5 : 3

Answer - (5/3)

Posted from my mobile device

Regor60 · Answer

An insight could be that at the point of contact the speed of that point of tangency has to be the same for each gear, otherwise there would be slippage between the gears.

Speed is rotations/minute * distance/rotation, so

RPM(A)*2piR(A) = RPM(B)*2piR(B) so

RPM(A)/RPM(B) = R(B)/R(A)

= 50/30

Posted from my mobile device

Dauan · Answer

The questions does not specify that the rate circumferential rate ≠ 0. Therefore, the ratio could be 5:3 or undefined.

Ans E.

Please let me know if I am mistaken.

napolean92728 · Answer

We are given two interconnected circular gears, Gear A and Gear B, which move at the same  circumferential speed . This means that the  linear speed  (distance traveled along the edge per unit time) of both gears is the same.
 Step 1: Given Values 
 
 Diameter of  Gear A  =  30 cm  
 Diameter of  Gear B  =  50 cm

From the diameter, we can determine the  circumference  of each gear using the formula:  C=π×D 
Thus:
 
 Circumference of  Gear A  =  π×30=30π cm  
 Circumference of  Gear B  =  π×50=50π cm

Step 2: Understanding Revolutions 
Each time a gear completes  one full revolution , it travels a distance equal to its  circumference . Since the gears are interconnected, the  linear speed  at the contact point is the same for both.
Let’s define:
 
  N_A  = Number of revolutions per minute for Gear A 
  N_B  = Number of revolutions per minute for Gear B  
Since both gears move with the same  linear velocity , we have the relation:
 N_A 	imes C_A = N_B 	imes C_B 
Substituting the values of the circumferences:
 N_A 	imes 30\pi = N_B 	imes 50\pi 
Canceling  π  from both sides:
 N_A 	imes 30 = N_B 	imes 50

Step 3: Solving for the Ratio 
Rearrange the equation to find the ratio:
 \frac{N_A}{N_B} = \frac{50}{30} = \frac{5}{3} 
Thus, the ratio of the number of revolutions of Gear A to Gear B is  5:3 .

Two interconnected, circular gears travel at the same circumferential

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Two interconnected, circular gears travel at the same circumferential

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