# The velocity ratio of two pulleys connected by an open belt or crossed belt is

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The velocity ratio of two pulleys connected by an open belt or crossed belt is

(a) directly proportional to their diameters

(b) inversely proportional to their diameters

(c) directly proportional to the square of their diameters

(d) inversely proportional to the square of their diameters

My question is based upon Belt, Rope and Chain Drives topic in portion Belt, Rope and Chain Drives of Machine Kinematics

by (106k points)
The correct option is (b) inversely proportional to their diameters

To explain I would say: It is the ratio between the velocities of the driver and the follower or driven.

Let d1 = Diameter of the driver,

d2 = Diameter of the follower,

N1 = Speed of the driver in r.p.m., and

N2 = Speed of the follower in r.p.m.

∴ Length of the belt that passes over the driver, in one minute

= π d1.N1

Similarly, length of the belt that passes over the follower, in one minute

= π d2 . N2

Since the length of belt that passes over the driver in one minute is equal to the length of belt that passes over the follower in one minute, therefore

π d1.N1 = π d2 . N2

∴ Velocity ratio,     N2/N1 = d1/d2.

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