A body of mass 120g placed at the 10cm mark on a uniform metre rule makes the rule settle horizontally on a…

Analyze the question: A uniform metre rule balances horizontally on a pivot at the 35 cm mark, with a 120 g mass hung at the 10 cm mark. We need the mass of the rule.

Concept: This uses the principle of moments. For equilibrium, the clockwise moments equal the anticlockwise moments about the pivot. The weight of a uniform rule acts at its centre, which is the 50 cm mark.

Solution:

• Distance of the 120 g mass from the pivot = 35 − 10 = 25 cm (on the left)
• Distance of the rule's centre of gravity from the pivot = 50 − 35 = 15 cm (on the right)

Let the mass of the rule be M.

Anticlockwise moment = clockwise moment

120 × 25 = M × 15

3000 = 15M

M = 200 g

Answer: The mass of the rule is 200 g, which is option D.

Tip: In balancing-rule questions, always do three things:

1. Place the rule's weight at the 50 cm mark.
2. Measure every distance from the pivot, not from the end of the rule.
3. Set the moments on each side equal.