A meter stick has a mass of 0.24 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 12.0 cm toward the end with the chain. Determine the mass of the chain.

When balanced, the clockwise moment about the balance point equals the

anticlockwise moment.

Reasons:

The mass of the meter stick, = 0.24 kg

Change in the position of the balance point = 12.0 cm towards the end with the chain

Required:

The mass of the chain

Solution:

Initial position of balance point = 50 cm from each end

New position of balance point from the end with the chain = 50 - 12 = 38

Therefore;

New position of balance point from the end with the chain, = 38 cm

Position where the mass of the stick acts = The middle (50 cm from each end)

Length from the center of mass of the stick to the balance point, = 12 cm

When the meter stick is balanced, we have;

× = ×

Where;

= The mass of the chain

Which gives;

0.24 kg × 12 cm = × 38 cm

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The mass of the chain is 75.7 grams

Explanation:

Let the mass of chain be M

Mass of stick = m = 0.24  kg

We are given that When a small chain is suspended from one end, the balance point moves 12.0 cm toward the end with the chain

x= 12 cm = 0.12 m

Length of stick L = 1m

Balancing the moment of force about the pivot we have

0.0757=M

75.7 grams=M

Hence  the mass of the chain is 75.7 grams

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