Question

A pulley system has a single fixed pulley and a single movable pulley. Find out its mechanical advantage.
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint: Mechanical advantage is the ratio of load attached to the effort applied on the pulley. We can design a certain number of systems which provide us an advantage that we can lift an object by applying a force, lesser than the weight of the object itself. Hence mechanical advantage is the measure of how much one has to apply a force to lift a particular weight. Special arrangement of pulleys can help us in lifting the weights with less effort than directly lifting it.

Complete answer:
 In the diagram, ‘E’ is the applied effort, ‘T’ is the tension in the light inextensible string and ‘L’ is the load attached to the movable pulley. Consider the situation at equilibrium. We can see that at equilibrium, net force in the string is zero. Now, we will write the equilibrium equations for different strings.
Hence Effort ‘E’ = T
And for movable pulley, L = T+T = 2T
Now, by the definition of mechanical advantage $M.E={\displaystyle \frac{load}{effort}}={\displaystyle \frac{L}{E}}={\displaystyle \frac{2T}{T}}=2$
Hence, in the system of one movable and one fixed pulley, mechanical advantage is 2.

So, the correct answer is “Option B”.

Note:
Here, we had considered that the pulley is light and frictionless and also the strings are light. Hence the mechanical advantage came out to be 2. But practically this is not the case. Hence the actual mechanical advantage is always less than two. However this phenomenon is very useful in factories where we have to lift huge weights very delicately. By attaching more movable pulleys, we can further increase the mechanical advantage of the system to any desired value.