Question

What is meant by torque due to gravity?

Answer 1

For gravitational torque we consider the force is acting at certain point where the whole mass can be confirmed (centre of mass).

Now,

$\overrightarrow{\tau }=\int d\tau =\int \overrightarrow{r}\times d\overrightarrow{mg}$

As we know,

$\overrightarrow{r}cm=\frac{1}{M}\int \overrightarrow{r}dm$

Therefore,

$\overrightarrow{\tau }=M{\overrightarrow{r}}_{cm}\times \overrightarrow{g}$

$=\overrightarrow{r}cm\times Mg$

Which is the desired result.