Question

In a simple machine, if the effort arm is doubled and the load arm is halved, then how does the velocity ratio (VR) change?

• A. Becomes 2 times the initial value.
• B. Becomes 4 times the initial value.
• C. Becomes half of the initial value.
• D. Remains the same.

Answer 1

The correct option is B

Becomes 4 times the initial value.

We know that, velocity ratio = $\frac{Effortarm}{Loadarm}$

Let the initial length of effort arm be EA and initial length of load arm be LA.

Initial velocity ratio = $\frac{Effortarm}{Loadarm}$ = $\frac{EA}{LA}$

Now, length of final effort arm = 2 x initial length = 2 EA
And length of the final load arm = $\frac{initiallength}{2}=\frac{LA}{2}$

So, final velocity ratio = $\frac{finaleffortarm}{finalloadarm}=\frac{2EA}{LA/2}$
= $\frac{4EA}{LA}$

Hence the final velocity ratio is 4 times the initial velocity ratio.