The two pulleys having radii of 15 cm and 8 cm, respectively are connected by a belt as shown in the figure. The larger pulley rotates 25 times in 36 seconds . What is the frequency of rotation of the smaller pulley ?
the smaller wheel rotates 15/8 as fast as the larger wheel.
So, 15/8 * 25rev/36s = (15*25)/(8*36) = 375/288 rev/s
To find the frequency of rotation of the smaller pulley, we first need to determine the number of rotations it makes in the given time period.
We know that the larger pulley rotates 25 times in 36 seconds.
Next, we can find the ratio of the radii of the two pulleys.
The radius of the larger pulley is 15 cm, and the radius of the smaller pulley is 8 cm.
Thus, the ratio of their radii is 15/8.
Since the belt connects the pulleys, the ratio of their rotations will be the same as the ratio of their radii.
Now we can calculate the number of rotations of the smaller pulley.
The number of rotations of the smaller pulley = (number of rotations of the larger pulley) x (ratio of radii)
Number of rotations of the smaller pulley = 25 x (8/15)
Finally, we can calculate the frequency of rotation of the smaller pulley.
Frequency = (number of rotations) / (time in seconds)
Frequency = (number of rotations of the smaller pulley) / 36
By plugging in the values, we get:
Frequency = (25 x 8/15) / 36
Simplifying further, we find the frequency of rotation of the smaller pulley.