A wheel and axle system consists of a wheel with a radius of 25\text{ cm} attached to an a… — JAMB UTME

A wheel and axle system consists of a wheel with a radius of $25\text{ cm}$ attached to an axle with a radius of $5\text{ cm}$ . What is the velocity ratio of this machine?

Answer: 5

Answer

The velocity ratio of the machine is 5.

The velocity ratio (VR) of a wheel and axle is the ratio of the radius of the wheel (

R

) to the radius of the axle (

r

). Calculating

\frac{25\text{ cm}}{5\text{ cm}}

gives a velocity ratio of

5

Step-by-Step Solution

Identify the formula for the velocity ratio of a wheel and axle system.

\text{VR} = \frac{R}{r}

Velocity ratio is defined as the distance moved by the effort (proportional to wheel radius) divided by the distance moved by the load (proportional to axle radius).

Substitute the given values into the formula.

\text{VR} = \frac{25\text{ cm}}{5\text{ cm}}

The radius of the wheel

R = 25\text{ cm}

and the radius of the axle

r = 5\text{ cm}

Calculate the final ratio.

\text{VR} = 5

Dividing 25 by 5 yields 5. The ratio is dimensionless because the units of centimeters cancel out.

Key Concept

Velocity Ratio of a Wheel and Axle

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