Question

A metre stick is balanced on a knife-edge at its centre. When two coins, each of mass $5\, g$ are put one on top of the other at the $12\,cm$ mark, the stick is found to be balanced at $45.0\,cm$ . What is the mass (in gram ) of the metre stick?

Answer 1

Let total mass of the metre stick be $M$ gram

Distance between mid-point $E$ and new centre of gravity ( $DE$ ),
$=50-45=5\, cm$
Distance between $12cm$ mark and new centre of gravity ( $CD$ ),
$=45-12=33\, cm$
From the principle of moments in equilibrium,
$Mg\times DE=\left(\right.2\times 5g\left.\right)\times CD$
$M\times 5=10\times 33$
or $M=66\, g$
$\therefore$ Mass of the metre stick is $66\,g$ .