Question

A perfect machine has
A) $VR = MA$
B) $VR > MA$
C) $VR < MA$
D) None of the above

Answer 1

Hint: Here ${\text{MA}}$ represents the mechanical advantage of the machine and ${\text{VR}}$ represents the velocity ratio of the machine. The efficiency of a simple machine refers to the ratio of the mechanical advantage to its velocity ratio. For an ideal machine, the efficiency of the machine will be one.

Formula used:
The efficiency of a machine is given by, $\eta = \dfrac{{MA}}{{VR}}$ where ${\text{MA}}$ is the mechanical advantage and ${\text{VR}}$ is the velocity ratio of the machine.

Complete step by step answer:
Step 1: Express the efficiency of a perfect machine.
The efficiency of a machine can be expressed as $\eta = \dfrac{{MA}}{{VR}}$ where ${\text{MA}}$ is the mechanical advantage and ${\text{VR}}$ is the velocity ratio of the machine.
For a perfect machine, the efficiency is one i.e., $\eta = 1$ .
Then we have the efficiency of an ideal machine as $\eta = \dfrac{{MA}}{{VR}} = 1$
$ \Rightarrow VR = MA$
i.e., the velocity ratio of the machine will be the same as that of the mechanical advantage.

So the correct option is (A).

Additional information:
A perfect machine or an ideal machine is a mechanical concept in which the energy lost or power dissipated by the working of the machine is zero. There are six simple machines to be exact and they are the inclined plane, wheel and axle, pulley, lever, screw and wedge. Compound machines which are essentially a combination of two or more simple machines also exist.

Note: A machine usually involves the lifting of a load. The mechanical advantage of a machine is the ratio of the load to be lifted to the effort applied to lift the load. Velocity ratio refers to the ratio of the displacement of the effort to the displacement of the load in the simple machine. A simple machine essentially tries to reduce the work done by a person.