Q109 / 200 · NEET 2009 (Screening) · Physics

If $\overrightarrow{\mathrm{F}}$ 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
    $\overrightarrow{\mathrm{r}} \cdot \vec{\tau} \neq 0$ and $\overrightarrow{\mathrm{F}} \cdot \vec{\tau}=0$
  • B
    $\overrightarrow{\mathrm{r}} \cdot \vec{\tau}>0$ and $\overrightarrow{\mathrm{F}} \cdot \vec{\tau} < 0$
  • Correct answer
    C
    $\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0$ and $\overrightarrow{\mathrm{F}} \cdot \vec{\tau}=0$
  • D
    $\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0$ and $\overrightarrow{\mathrm{F}} \cdot \vec{\tau} \neq 0$

Solution

Key Idea Torque is an axial yector ie, its direction is always perpendicular to the plane containing vectors $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{F}}$. $$ \vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}} $$ Torque is perpendicular to both $\vec{r}$ and $\vec{F}$ $$ \therefore \quad \begin{aligned} \vec{\tau} \cdot \overrightarrow{\mathrm{r}} & =0 \\ \overrightarrow{\mathrm{F}} \cdot \vec{\tau} & =0 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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