A uniform metre rule of mass 120\text{ g} is balanced horizontally on a pivot placed at th… — JAMB UTME

A uniform metre rule of mass $120\text{ g}$ is balanced horizontally on a pivot placed at the $40\text{ cm}$ mark when an unknown mass $m$ is suspended at the $10\text{ cm}$ mark. What is the value of the mass $m$ in grams?

Answer: 40 g

Answer

The mass

m

required to balance the metre rule horizontally is

40\text{ g}

According to the Principle of Moments, a system is in rotational equilibrium when the sum of anticlockwise moments equals the sum of clockwise moments about the pivot. The weight of the

120\text{ g}

uniform metre rule acts at its center of gravity (

50\text{ cm}

mark), which is

10\text{ cm}

to the right of the pivot at

40\text{ cm}

. This creates a clockwise moment of

120\text{ g} \times 10\text{ cm} = 1200\text{ g}\cdot\text{cm}

. The mass

m

is suspended at the

10\text{ cm}

mark, which is

30\text{ cm}

to the left of the pivot, creating an anticlockwise moment of

m \times 30\text{ cm}

. Setting

30m = 1200

yields

m = 40\text{ g}

Step-by-Step Solution

Determine the position of the center of gravity of the metre rule.

Center of gravity is at the

50\text{ cm}

mark.

A uniform metre rule has its weight concentrated at its geometric midpoint.

Calculate perpendicular distances from the pivot at

40\text{ cm}

to all acting forces.

Distance to rule weight =

50\text{ cm} - 40\text{ cm} = 10\text{ cm}

; Distance to mass

m

40\text{ cm} - 10\text{ cm} = 30\text{ cm}

Moments are calculated by multiplying force (or mass) by perpendicular distance from the turning point.

Apply the Principle of Moments for equilibrium.

Sum of anticlockwise moments = Sum of clockwise moments

\implies m \times 30 = 120 \times 10

For rotational equilibrium, the total clockwise moment must equal the total anticlockwise moment about the pivot.

Solve for the unknown mass

m

m = 40\text{ g}

Dividing

1200\text{ g}\cdot\text{cm}

30\text{ cm}

gives

40\text{ g}

Key Concept

Principle of Moments and Center of Gravity of a Uniform Body

Estimated Time:50s

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