Two pulleys one with adius 2 inches and the other with radius 8 inches are connected by a belt. If the 2 inch pulley is caused to rotate at 3 revolutions per minuite detirmine te revolutions per minute of the 8 inch pulley

Explanation:

we know that,

linear speed = circumference × revolution per minute

linear speed of belt = 2πr × revolution per minute

now we will compute the linear speed of a belt for 2 inch pulley that is,

linear speed for 2 inch pulley = (2π×2)×( 3 revolutions per minute)  ∵ r =2

                                              = 4π × 3 revolution per minute    (1)

again we will compute the linear speed of a belt for 8 inch pulley,

linear speed of 8 inch pulley = (2π×8) × (x revolution per minute) ∵ r =8

                                            = 16π×x revolutions per minute      (2)

As the linear speed is same for both pulleys. by comparing equations (1) and (2).

                           4π×3 = 16π×x

                              x = 3/4

Thus, the revolutions per minute for the 8 inch pulley is 3/4.