Question

Two wheel gears are connected by a chain. The larger gear has a radius of 8 centimeters and the smaller gear has a radius of 3 centimeters. The smaller gear completes 24 revolutions in 20 seconds.
What is the linear velocity of each of the gears in centimeters per minute?

A.The linear velocity of the smaller gear is 144π centimeters per minute. The linear velocity of the larger gear is 54π centimeters per minute.
B.The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute.
C. The linear velocity of the gears is the same. The linear velocity is 7.2π centimeters per minute.
D. The linear velocity of the smaller gear is 432π centimeters per minute. The linear velocity of the larger gear is 144π centimeters per minute.

Please any help would be much appreciated. will mark as brainiest

Answer 1

Answer:

B.The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute.

Explanation:

As we know that the small gear completes 24 revolutions in 20 seconds

so the angular speed of the smaller gear is given as

$\omega = 2\pi\frac{24}{20}$

$\omega = 2.4\pi rad/s$

Now we know that the tangential speed of the chain is given as

$v = r \omega$

so we have

$v = (3 cm)(2.4\pi)$

$v = 7.2 \pi cm/s$

$v = 432\pi cm/min$

Since both gears are connected by same chain so both have same linear speed and hence correct answer will be

B.The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute.