To measure the mass of a metre rule by using a single known mass

A metre rule is supported in a loop of thread hung from a clamp and stand and dusted until it balances horizontally. The loop will then be at the centre of gravity, G. of the rule. If the rule is not of uniform thickness (few rules are) the centre of gravity will not be at the 50 em mark. However, this will not affect the accuracy of he experiment so long as the correct position is noted and later used in the calculation. A 0.1 kg mass is now hung from the rule by thread at a point near one end. The position of the rule in the supporting loop is then adjusted until it again balances, horizontally (Fig. 6.11). Let the mass of the rule be m kg. The rule is now in equilirium under the action or two moments about the supporting loop. namely. that or
It own force of gravity mg acting through the centre of gravity G and the weight of the 0.1 kg mass on the opposite side.

If d, and d2 respectively are the distances of G and the 0.1 kg mass from the loop, then equating moments we have

mg x d , = 0.1 g x d2
m = 0.1 x d2
d1
Iote that g disappears from the final calculation