Question

In the given figure, balancing of a cardboard on the tip of a pencil is done. The point of support, $G$ is the centre of gravity. Choose the correct option.

• A. ${\tau }_{Mg}$ about $CG=0$
• B. ${\tau }_R$ about $CG=0$
• C. Net $\tau$ due to $m_{1}g,m_{2}g\dots \dots m_{n}g$ about $CG=0$
• D. All of the above

Answer 1

Answer: (D)

Point $G$ is the centre of gravity of the cardboard and it is so located that the total torque on it due to forces $m_{1}g,m_{2}g\cdots m_{n}g$ is zero.
It means ${\tau }_{Mg}=\Sigma {\tau }_i=\Sigma r_i\times m_{i}g=0$.
$\tau$ of reaction $R$, i.e ${\tau }_R$ about $CG$ is also zero as it is at $CG$.
$\therefore CG$ could be defined as the point, where the total gravitational torque on the body is zero.