Question

“Perhaps the earliest work of Archimedes that we have is that on ‘Plane Equilibrium’. In this, some fundamental principles of mechanics are set forth as rigorous geometric propositions. The work opens with furious postulate ‘Equal weights at equal distances are in equilibrium; equal weights at unequal distances are not in equilibrium, but incline towards the weight at the greater distance.’
According to this passage, which factors determine equilibrium?

• A. weight
• B. distance
• C. weight & distance
• D. equality of weights & distances

Hint:

Equilibrium on a lever depends on the {moment} about the fulcrum: both weight and its arm.

Answer 1

The Correct Option is C

The passage from Archimedes' work on ‘Plane Equilibrium’ gives us insight into the factors that determine equilibrium. According to the passage, the equilibrium of weights is influenced by two main factors: weight and distance. These are explained as follows:

• Weight: The actual mass of the objects plays a crucial role. Equal weights mean that the masses being compared are identical, while unequal weights indicate different masses.
• Distance: The distance refers to how far each weight is situated from the point of support or fulcrum. This is critical because distance affects the torque exerted by the weights.

Archimedes postulates that for equilibrium, "equal weights at equal distances" will balance perfectly. In contrast, if these weights are at unequal distances, they will not achieve equilibrium and will instead tip towards the weight further from the fulcrum, as it exerts more torque. Therefore, the passage clearly demonstrates that both weight and distance are essential in determining equilibrium. Hence, the correct answer to the question is: weight & distance.