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The metre scale activity looks simple: hang two masses, slide them until the scale balances, multiply and divide. Yet viva and exam questions often turn it around: what if the wedge is not at the centre, or how heavy is the scale itself? This post explains the principle, works the standard method with sample readings, then uses the scale's own weight to find its mass.
Which syllabuses include this activity?
The CBSE Physics curriculum for 2026-27 lists, among the Class 11 activities: "To determine mass of a given body using a metre scale by principle of moments." The Syllabus for JEE (Main) 2026 includes "Metre scale - the mass of a given object by the principle of moments" as item 4 of its experimental skills unit, and the NEET (UG) 2026 syllabus lists the same item. The theory is section 6.8.1, Principle of moments, in the NCERT Class 11 chapter System of Particles and Rotational Motion.
What is the principle?
The NCERT Class 11 physics laboratory manual states it for this activity: "For a body free to rotate about a fixed axis, in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments." If a known mass M₁ hangs at distance l₁ on one side of the centre of gravity and the unknown M₂ at l₂ on the other, then M₂l₂ = M₁l₁. The factor g appears on both sides and cancels, so you can work in grams and centimetres.
The manual first balances the bare scale on the wedge and draws a line through the balance point, the centre of gravity. All distances are measured from that line. With the wedge there, the scale's weight acts through the pivot and has no moment.
Worked example 1: an unknown body by the standard method
Sample readings, with distances from the balance line:
50 g at l₁ = 29.9 cm balances the body at l₂ = 21.4 cm, so M₂ = 50 × 29.9 ÷ 21.4 ≈ 69.9 g.
60 g at l₁ = 25.0 cm balances it at 21.4 cm, so M₂ ≈ 70.1 g.
80 g at l₁ = 18.8 cm balances it at 21.4 cm, so M₂ ≈ 70.3 g.
Mean: about 70.1 g. The manual asks for repeats with "a slightly lighter and a heavier weight" for exactly this reason: the spread of the three values shows how good your readings are.
Worked example 2: the mass of the scale itself
Now use the scale's weight on purpose. A uniform scale balances on its own at the 50.0 cm mark. Hang a 100 g mass at the 10.0 cm mark and slide the scale over the wedge until it balances again. Suppose (sample reading) the new balance point is the 32.5 cm mark.
The 100 g mass is 32.5 − 10.0 = 22.5 cm on one side of the wedge.
The scale's weight acts at its centre of gravity, 50.0 − 32.5 = 17.5 cm on the other side.
Moments: M × 17.5 = 100 × 22.5, so M = 2250 ÷ 17.5 ≈ 129 g.
A quick check: if the scale weighed exactly 100 g, the balance point would sit halfway between 10 cm and 50 cm, at 30 cm. A heavier scale pulls the balance point towards its own centre, and 32.5 cm is on that side.
What if you assume the centre of gravity is at 50 cm?
Real scales are not perfectly uniform. Suppose the 129 g scale actually balances at 50.6 cm, but you put the wedge at the 50.0 cm mark without checking. The scale's weight now has a moment of about 129 × 0.6 ≈ 77 g cm. In the first reading of example 1, the known mass supplies 50 × 29.9 = 1495 g cm, so the stray moment is about 5 percent of it and shifts the answer by roughly 3.6 g. That is why the manual has you find the balance line first.
How accurate is the result?
A metre scale reads to 0.1 cm. For the third reading of example 1, the fractional error in M₂ is about 0.1/18.8 + 0.1/21.4 ≈ 1.0 percent, or about ±0.7 g. The three results span 69.9 to 70.3 g, which fits. Longer lever arms make the fractional error smaller, so keep the masses well away from the wedge.
Which mistakes cost marks?
Measuring from the zero end of the scale instead of from the wedge.
Assuming the centre of gravity is at 50 cm without balancing the bare scale.
Reading the loop position at its edge rather than the thread's centre, and letting threads hang at an angle.
Converting to newtons halfway. Either keep g throughout or drop it throughout.
Our post on centre of gravity and centre of mass explains why the balance point of a scale on a lab bench is also its centre of mass. For harder statics, see torque and equilibrium problems with ladders and beams.
If moments still feel like a formula rather than an idea, the Fermi Concept Library covers every concept in physics, each with its own lesson, so you can revise torque before the practical.
A practice routine
Day 1: Write the principle in the manual's words and explain why g cancels.
Day 2: Redo example 2 with 50 g at the 10 cm mark. If the scale is 129 g, the balance point should be near the 38.8 cm mark.
Day 3: Two problems with a non-uniform scale whose centre of gravity is not at 50 cm.
Before your practical, balance a ruler on a pencil at home with a coin taped near one end and find the ruler's mass from the shift.
