To find the mass of an object by means of a metre rule

A metre rule with a small hole drilled near its centre as described on page 62 can be used in conjunction with a single known mass to measure the mass of an object. Having balanced the rule on a knitting needle as described on page 62, the known
mass and the object whose mass is to be found are suspended from the rule by cotton loops, one on either side of the pivot. Their distances from the pivot are then adjusted until the rule once more balances horizontally (Fig. 6.9).

Maximum accuracy will be obtained if these distances are made as large as possible. Since it is inevitable that a small error will be made when the distances of the weights from the pivot are measured, the percentage error in the final result will be less if large distances are used rather than small ones. Suppose that, in a particular experiment, a 0.1 kg mass placed 45 cm from the pivot balances an object of unknown mass m placed 20.5 em from the pivot on the opposite side of the rule. Applying the principle of moments

Note that g disappears from the final calculation. As an exercise, this method should be used to find the masses of a number 0 different objects and the results recorded in a table as below,