Determination of weight of an object using the principle of moments
Chapter: 10th Science : Physics Practicals
Aim
To determine the weight of an object using the principle of moments
Apparatus Required
A metre scale, a knife edge, slotted weights, thread
Procedure
- A metre scale is supported at its centre of gravity by a knife edge or suspended by using a thread tied to its centre so that the scale is in the horizontal position. Ensure that the scale is in equilibrium position.
- A known weight \(W_2\) and an unknown weight \(W_1\) are suspended from to either side of the the scale using the weight hangers.
- Fix the position of one weight hanger and adjust the position of the second weight hanger such that the scale is in equilibrium.
- Measure the distance \(d_1\) and \(d_2\) of the two weight hangers from the centre of the scale accurately.
- The experiment is repeated for different positions of the unknown weight. Measure the distances. The reading are tabulated as follows:
Observation
Calculations
Moment of a force can be calculated using the formula:
Moment of the force = Force × distance
Clock wise moment by unknown weight = \(W_1 \times d_1\)
Anticlockwise moment by known weight = \(W_2 \times d_2\)
According to the principle of moments, for equilibrium:
$$W_1 \times d_1 = W_2 \times d_2$$
w1 w2
Therefore, the unknown weight can be calculated as:
$$ \text{Unknown weight } (W_1) = \frac{W_2 \times d_2}{d_1} $$
Result
Using the principle of moments, the weight of the unknown body \(W_1\) = ……. Kg Wt.