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 $\vec{F} \cdot \vec{\tau}=0$