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

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.