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.
