Moments in Rotational Equilibrium

Steps:

• Moments cause rotation; for equilibrium, net moment about a point is zero.
• This means sum of counterclockwise moments equals sum of clockwise moments about the same point.
• The student's statement equates counterclockwise moments about X to clockwise moments about Y.
• Equality holds generally only if X and Y coincide, making it the standard equilibrium condition.

Why D is correct:

• By the principle of moments, rotational equilibrium requires sum of counterclockwise moments to equal sum of clockwise moments about the identical point, so X must equal Y.

Why the others are wrong:

• A: Center of gravity balances forces but does not equate moments about distinct points X and Y.
• B: Pivot ensures zero net moment at that point, but only for moments calculated about it, not a different point.
• C: Opposite ends may relate to lever arms but do not guarantee equality of specified moment sums.

Final answer: D