To determine the mass of two different objects using a beam balance.

• Beam balance
• Standard masses (weights)
• Two objects of unknown mass
• Forceps (to handle weights)
• Weighing box
• Tissue paper/soft cloth (for cleaning)

A beam balance works on the principle of moments. It consists of a horizontal beam supported at the center by a fulcrum. The beam has two pans of equal mass suspended at equal distances from the fulcrum. When no masses are placed on either pan, the beam stays in a horizontal position.

When an object is placed on one pan, the beam tilts. To measure the mass of this object, standard masses are placed on the other pan until the beam becomes horizontal again. At equilibrium, the moments about the fulcrum are equal on both sides.

According to the principle of moments:

Since the distances \(d_1\) and \(d_2\) from the pans to the fulcrum are equal:

Therefore, the mass of the unknown object equals the sum of the standard masses placed on the other pan when the beam is horizontal.

The mass of the unknown object is given by:

Where:

• \(M_{object}\) = Mass of the object being measured
• \(\sum M_{standard}\) = Sum of the standard masses used to balance the beam

1. Setting up the balance:
   • Place the beam balance on a level, stable surface.
   • Check that the beam is horizontal when unloaded by adjusting the leveling screws if necessary.
   • Ensure the pointer at the center of the beam aligns with the zero mark when unloaded.
2. Measuring the first object:
   • Place the first object on the left pan of the balance.
   • Using forceps, carefully place standard masses on the right pan until the beam is balanced (pointer at zero).
   • Start with larger masses and progressively add smaller ones as needed.
   • Note the total mass of the standard weights used.
3. Measuring the second object:
   • Remove the first object and all standard masses.
   • Check that the unloaded balance returns to equilibrium.
   • Place the second object on the left pan.
   • Repeat the balancing process with standard masses.
   • Note the total mass of the standard weights used.
4. Repeated measurements:
   • Repeat the measurement for each object two more times.
   • Calculate the average mass for each object.

For each object, calculate the average mass from the three trials:

Where \(m_1\), \(m_2\), and \(m_3\) are the masses measured in trials 1, 2, and 3 respectively.

Example Calculation:

Suppose for Object 1, the masses measured in the three trials are:

• Trial 1: 45.5 g
• Trial 2: 45.7 g
• Trial 3: 45.6 g

The average mass would be:

The masses of the two objects as determined using the beam balance are:

• Mass of Object 1: ____________ g
• Mass of Object 2: ____________ g

1. Ensure the balance is placed on a level, stable surface.
2. Check that the balance is properly adjusted and reads zero when unloaded.
3. Handle the weights with forceps to prevent contamination from oils on fingers.
4. Place weights gently on the pan to avoid damaging the balance.
5. Add or remove weights only when the balance is arrested (if it has an arresting mechanism).
6. Avoid air currents around the balance during measurements.
7. Make sure the object being weighed is clean and dry.
8. Return all weights to their proper places in the weight box after use.
9. Record readings only after the balance has come to a complete rest.

1. Instrumental Errors:
   • Unequal arm lengths of the balance
   • Inaccuracy in the standard masses
   • Friction at the knife edges or fulcrum
2. Observational Errors:
   • Parallax error in reading the pointer position
   • Misjudging when the beam is perfectly horizontal
3. Environmental Errors:
   • Air currents affecting the balance
   • Temperature variations causing expansion/contraction of the balance parts
   • Vibrations from surroundings
4. Procedural Errors:
   • Improper handling of weights
   • Dust or fingerprints on the weights or objects
   • Electrostatic charges on the object or balance