Explain the principle of moments of rotational equilibrium? Hence define mechanical advantage?

Explanation

Let us consider a light rod of negligible mass which is pivoted at a point along its length. Let two parallel forces `F_(1)` and `F_(2)` act at the two ends at distances `d_(1)` and `d_(2)` from the point of pivot and the normal reaction force N at the point of pivot as shown in the figure (Principle of moments).
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If the rod has to remain stationary in horizontal positon, then it should be in traslational and rotaional equilibrium. Then both the net force and net torque must be zero.
For net force to be zero, `-F_(1)+N-F_(2)=0`
`=F_(1)+F_(2)`
For net torque to be zero `d_(1)F_(1)-d_(2)F_(2)=0`
`d_(1)F_(1)=d_(2)F_(2)`............1
Equation 1 represents the principle of moments. This forms the principle for beam balance used for weighing goods with the condition `d_(1)=d_(2),F_(1)=F_(2)`. We can rewrite the equation 1 as
`(F_(1))/(F_(2))=(d_(2))/(d_(1))`
If `F_(1)` is the load and `F_(2)` is our effort, we get advantage when `d_(1)ltd_(2)`. This implies that `F_(1)gtF_(2)`. Hence we could lift a large load with small effort. The ratio `((d_(2))/(d_(1)))` is called mechanical advantage of the simple lever.