First slide

Torque

Question

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

Easy

A

$\vec{r} . \vec{τ} not equal to zero and \vec{F} . \vec{τ} = 0$
B

$\vec{r} . \vec{τ} > 0 and \vec{F} . \vec{τ} < 0$
C

$\vec{r} . \vec{τ} = 0 and \vec{F} . \vec{τ} = 0$
D

$\vec{r} . \vec{τ} = 0 abd \vec{F} . \vec{τ} not equal to zero$

Solution

Torque is an axial vector, i.e., its direction is always perpendicular to the plane containing vectors $\vec{r} and \vec{F}$ .
$\vec{τ} = \vec{r} \times \vec{F}$
Torque is perpendicular to both $\vec{r} and \vec{F}$
$\vec{τ} . \vec{r} = 0$
$\vec{F} . \vec{τ} = 0$

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