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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Rotational Motion

NEET 2009 · Physics · Rotational Motion

If F is the force acting on a particle having position vector r and...

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

Options

  1. Ar→⋅τ⃗≠0\overrightarrow{\mathrm{r}} \cdot \vec{\tau} \neq 0 and F→⋅τ⃗=0\overrightarrow{\mathrm{F}} \cdot \vec{\tau}=0
  2. Br→⋅τ⃗>0\overrightarrow{\mathrm{r}} \cdot \vec{\tau}>0 and F→⋅τ⃗<0\overrightarrow{\mathrm{F}} \cdot \vec{\tau} < 0
  3. Cr→⋅τ⃗=0\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0 and F→⋅τ⃗=0\overrightarrow{\mathrm{F}} \cdot \vec{\tau}=0
  4. Dr→⋅τ⃗=0\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0 and F→⋅τ⃗≠0\overrightarrow{\mathrm{F}} \cdot \vec{\tau} \neq 0

Correct answer

C. r→⋅τ⃗=0\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0 and F→⋅τ⃗=0\overrightarrow{\mathrm{F}} \cdot \vec{\tau}=0

Step-by-step solution

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