Question

State the Law of lever.
A. A lever is a rigid bar which is capable of turning about a fixed axis.
B. For a lever, clockwise moment of load about the fulcrum equals anticlockwise moment of effort about the fulcrum.
C. The mechanical advantage of a lever is equal to the ratio of the length of its effort arm to the length of its load arm.
D. None of the above

Answer 1

Hint: The main function of the lever is to produce an output force for a given applied input force. Here, the concept to be used is the moment of force. The moment of the effort force and the resistance force add up to zero.

Complete step by step answer:
- A Lever is a machine which consists of a rigid rod pivoted at a hinge or a fulcrum. Consider a load kept at a distance of ${d_1}$ and a force is applied on the other side of the fulcrum at a distance of ${d_2}$. The force applied is the input force and the resistive force applied by the lever is called the output force.. The distance between the point of contact of the input force and the fulcrum which is ${d_2}$, is called the effort arm. And the distance between the point where the resistive/output force acts and the fulcrum is called as the load arm.
- The mechanical advantage can be considered as the factor of amplification because it gives the factor by which the input force should be multiplied in order to get a force which cancels the moment of the input force.
- The Law of Lever states that the mechanical advantage is the ratio of the length of the effort arm to the length of the load arm.
- At equilibrium, the moment/torque of the two input and output forces about the fulcrum adds to zero. Mathematically,
$
  {N_i} + {N_o} = 0 \\
\implies {N_i} = {F_i}{d_2} \\
\implies {N_o} = {F_o}{d_1} \\
 \implies {F_i}{d_2} - {F_o}{d_1} = 0 \\
  \therefore \dfrac{{{F_i}}}{{{F_o}}} = \dfrac{{{d_1}}}{{{d_2}}} \\
 $
As you can see, the ratio is of great importance as it tells us the amplification factor.
Hence, the Law of Lever states that “the mechanical advantage of a lever is equal to the ratio of the length of its effort arm to the length of its load arm”.

So, the correct answer is “Option C”.

Note:
The resistive force is such that it cancels the moment of the input force by amplification of the force, changing the direction of the force and changing the point of contact of the force.The rigid can rotate about the fulcrum. And the clockwise moment of load about the fulcrum equals an anticlockwise moment of effort about the fulcrum. But the Law of Lever only states the mechanical advantage.