Q

# Stuck here, help me understand: - Motion of System Of Particles and Rigid Body - NEET

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

• Option 1)

$\vec{r}.\vec{t}>0\: and \: \vec{F}.\: \vec{t}<0$

• Option 2)

$\vec{r}.\vec{t}=0\: and\: \vec{F}.\vec{t}=0$

• Option 3)

$\vec{r}.\vec{t}=0\: and\: \vec{F}.\vec{t}\neq 0$

• Option 4)

$\vec{r}.\vec{t}\neq 0 and \vec{F}.\vec{t}=0$

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As discussed in

Torque -

$\underset{\tau }{\rightarrow}= \underset{r}{\rightarrow}\times \underset{F}{\rightarrow}$

- wherein

This can be calculated by using either  $\tau=r_{1}F\; or\; \tau=r\cdot F_{1}$

$r_{1}$ = perpendicular distance from origin to the line of force.

$F_{1}$ = component of force perpendicular to line joining force.

$\bar \tau= \bar r \times \bar f\:\:\:\:\Rightarrow \bar r.\bar \tau=0\:\:\:\:\bar F. \bar \tau=0$

Since, $\tau$ is perpendicular to the plane of $\bar r$ and $\bar F$

Hence the dot product of $\bar \tau$ and $\bar r$ and $\bar F$ is zero.

Option 1)

$\vec{r}.\vec{t}>0\: and \: \vec{F}.\: \vec{t}<0$

This option is incorrect.

Option 2)

$\vec{r}.\vec{t}=0\: and\: \vec{F}.\vec{t}=0$

This option is correct.

Option 3)

$\vec{r}.\vec{t}=0\: and\: \vec{F}.\vec{t}\neq 0$

This option is incorrect.

Option 4)

$\vec{r}.\vec{t}\neq 0 and \vec{F}.\vec{t}=0$

This option is incorrect.

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