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A simplistic yet realistic rendition of two pulleys connected by a belt. On one side, depict a larger pulley with a diameter of 9 inches, rotating rapidly at a speed indicating 1200 revolutions per minute. On the other side, illustrate a smaller pulley with a diameter of 6 inches. Avoid including any numerical values or text in the image. Focus on the mechanical nature of the setup, showing the belt connecting the two pulleys, offering the idea of rotational speed transfer between two different sized objects.

A pulley whose diameter is 9 inches is connected by a belt to another pulley whose diameter is 6 inches. If the larger pulley runs at 1200 revolutions per minute, at how many revolutions per minute does the smaller pulley run?

a. 800
b. 1080
c. 1600
d. 1800
e. 2000

please answer and explain

Since 9*2 = 6*3, the big pully turns 2 times while the small pulley turns 3 times

So, 3/2 * 1200 = 1800

Well, isn't this a pulley-dicious question! Let's get to the bottom of it, shall we?

We can use the principle of pulley speed ratios to solve this. The speed of the larger pulley is given as 1200 revolutions per minute. Now, since the pulleys are connected by a belt, their speeds are inversely proportional to their diameters.

So, the speed ratio can be found by dividing the diameter of the larger pulley (9 inches) by the diameter of the smaller pulley (6 inches), which gives us 1.5.

To find the speed of the smaller pulley, we need to multiply the speed of the larger pulley by the speed ratio. So, 1200 revolutions per minute multiplied by 1.5 gives us 1800 revolutions per minute.

Therefore, the answer is d. 1800 revolutions per minute. So, the smaller pulley is spinning at a clown-infused speed of 1800 RPM!

Hope that cleared things up while adding a touch of laughter to your day!

To find the revolutions per minute (RPM) of the smaller pulley, we can use the concept of ratio and proportion.

The ratio of the diameters of the two pulleys is 9 inches to 6 inches, or 3:2. This means that for every 3 revolutions of the larger pulley, the smaller pulley will make 2 revolutions.

Since the larger pulley is running at 1200 RPM, we can set up the following proportion:

3 revolutions of the larger pulley / 2 revolutions of the smaller pulley = 1200 RPM / x RPM (RPM of the smaller pulley)

Cross-multiplying, we get:

3x = 2 * 1200
3x = 2400

Dividing both sides by 3, we find:

x = 800

Therefore, the smaller pulley runs at 800 revolutions per minute.

So, the correct answer is option a. 800.

To find the answer to this question, we can use the concept of belt speed and the ratio of pulley diameters.

The belt speed is the same for both pulleys because they are connected by a belt. The belt speed is given by the formula:

Belt Speed = (Diameter of Pulley) x (Revolutions per Minute)

Let's denote the larger pulley with a diameter of 9 inches as 'Pulley A' and the smaller pulley with a diameter of 6 inches as 'Pulley B.'

For Pulley A:
Belt Speed of A = 9 inches x 1200 revolutions per minute
Belt Speed of A = 10800 inches per minute

Since the belt speed is the same for both pulleys, we can set up the following equation:

Belt Speed of A = Belt Speed of B

10800 inches per minute = (Diameter of B) x (Revolutions per Minute of B)

We know the diameter of B is 6 inches, so we can substitute that into the equation:

10800 inches per minute = 6 inches x (Revolutions per Minute of B)

Now, we can solve for the Revolutions per Minute of B:

Revolutions per Minute of B = 10800 inches per minute / 6 inches
Revolutions per Minute of B = 1800

Therefore, the smaller pulley, labeled Pulley B, runs at 1800 revolutions per minute.

The correct answer is d. 1800.