Mass by the principle of moments — practice questions

Question 1 · difficulty L1 · recall

For a body in rotational equilibrium about a pivot, the algebraic sum of moments is

• A. zero
• B. equal to its mass
• C. always clockwise
• D. always anticlockwise

Question 2 · difficulty L1 · understanding

The moment of a force about a pivot equals

• A. force divided by distance
• B. force times perpendicular distance from the pivot to its line of action
• C. mass times length only
• D. force times parallel distance

Question 3 · difficulty L2 · understanding

In a simple balance experiment, an unknown mass m at distance x balances known mass M at distance y when

• A. m/x=M/y
• B. mM=xy
• C. mx=My
• D. m+y=M+x

Question 4 · difficulty L2 · application

A 200 g mass at 30 cm balances an unknown mass at 20 cm. The unknown mass is

• A. 133 g
• B. 200 g
• C. 450 g
• D. 300 g

Question 5 · difficulty L3 · application

Why is it useful to choose the pivot as the moment reference?

• A. The pivot reaction has zero moment about the pivot
• B. Gravity disappears at the pivot
• C. all other forces become zero
• D. mass no longer has weight

Question 6 · difficulty L3 · application

A metre rule of non-negligible mass is used in a moments experiment. Its own weight acts effectively at

• A. the pivot always
• B. its centre of gravity
• C. the zero-cm mark always
• D. the heaviest attached mass

Question 7 · difficulty L4 · analysis

If the lever arm of an unknown mass is doubled while the balancing known mass and its arm are unchanged, the required unknown mass

• A. doubles
• B. quadruples
• C. halves
• D. is unchanged

Question 8 · difficulty L4 · analysis

A rule balances with equal masses placed at unequal distances from the pivot. This can occur if

• A. equal masses must always have equal distances regardless of rule mass
• B. gravity is different on the two sides
• C. moments do not depend on distance
• D. the rule's own weight contributes an additional moment

Question 9 · difficulty L5 · analysis

Which change improves precision in a principle-of-moments mass measurement?

• A. Using reasonably large lever arms while keeping the system stable and reading distances carefully
• B. Placing all masses nearly at the pivot
• C. allowing the rule to keep oscillating
• D. ignoring the rule's mass

Question 10 · difficulty L5 · analysis

An unknown mass m at 40 cm to the left of a pivot balances 100 g at 24 cm to the right, with the rule's own moment already compensated. m is

• A. 166.7 g
• B. 60 g
• C. 100 g
• D. 240 g