two pulley rotate at 150 rpm and 300 rpm. the diameter of the larger pulley 15cm if the pulley are connected by belt . what is the diameter of the smaller pulley.

Answer 1

Since the distance covered by the belt depends on the circumference of the circles , ...

150(2π(15)) = 300(2πr)
15π = 2πr
r = 15/2 = 7.5 cm

or

the speed of the pulleys is inversely proportional to the their radii

r/15 = 300/150
r/15 = 2
2r = 15
r = 7.5