In this post, we will find out the **equation of Efficiency** that relates **mechanical advantage and velocity ratio** of an **ideal machine.**

## Equation of Efficiency that relates mechanical advantage and velocity ratio of an ideal machine

The efficiency of a machine = Work output / Work input …. (1)

Now, Work output = Load x displacement of the load ….. (2)

And Work Input = Effort X displacement of the effort ….. (3)

From all 3 equations above,**Efficiency **= Work output / Work input = (Load x displacement of the load)**/**(Effort X displacement of the effort)

= (Load/Effort) x (displacement of load/displacement of effort)

= Mechanical Advantage x (1/Velocity Ratio) = Mechanical Advantage/Velocity Ratio **Efficiency= Mechanical Advantage/Velocity Ratio** = **MA/VR** …………………… (2)**For an ideal machine**, **Work output = Work input**

and hence **for an ideal machine** **efficiency = 1 **or 100%…. (3)

Hence, for an ideal machine from equation 2 and 3,**1 = MA/VR**

so, Hence, for an ideal machine **MA = VR**