Question

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

• A. $\vec{r}\cdot \vec{\tau }>0$ and $\vec{F}\cdot \vec{\tau }<0$
• B. $\vec{r}\cdot \vec{\tau }=0$ and $\vec{F}\cdot \vec{\tau }=0$
• C. $\vec{r}\cdot \vec{\tau }=0$ and $\vec{F}\cdot \vec{\tau }\ne 0$
• D. $\vec{r}\cdot \vec{\tau }\ne 0$ and $\vec{F}\cdot \vec{\tau }=0$

Answer 1

Answer: (B)

Torque is always perpendicular to $\vec{F}$ as well as $\vec{r}$.
$\therefore \vec{r}+\vec{\tau }=0$ as well as $\vec{F}\cdot \vec{\tau }=0$