Question

If $\overrightarrow{F}$ be a force acting on a particle having the position vector $\overrightarrow{r}$ and $\overrightarrow{\tau }$ be the torque of this force about the origin, then

• A. $\overrightarrow{\tau }.\overrightarrow{F}=0$ and $\overrightarrow{r}.\overrightarrow{\tau }=0$
• B. $\overrightarrow{\tau }.\overrightarrow{F}=0$ and $\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
• C. $\overrightarrow{r}.\overrightarrow{\tau }\ne 0$ and $\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
• D. $\overrightarrow{r}.\overrightarrow{\tau }\ne 0$ and $\overrightarrow{F}.\overrightarrow{\tau }=0$

Answer 1

The correct option is A $\overrightarrow{\tau }.\overrightarrow{F}=0$ and $\overrightarrow{r}.\overrightarrow{\tau }=0$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F},$ so $\overrightarrow{\tau }.\overrightarrow{F}=0$