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  • Need clarity, kindly explain! - Rotational Motion - JEE Main

Let \vec{F} be 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}\cdot \vec{T}= 0\: \: and\: \: \vec{F}\cdot \vec{T}\neq 0

 Option 2)

\vec{r}\cdot \vec{T} \neq0\: \: and\: \: \vec{F}\cdot \vec{T} = 0
Option 3)

\vec{r}\cdot \vec{T} \neq0\: \: and\: \: \vec{F}\cdot \vec{T} \neq 0

 Option 4)

\vec{r}\cdot \vec{T} = 0\: \: and\: \: \vec{F}\cdot \vec{T} = 0

Answers (1)

best_answer

As we learnt 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.

 

 

 

 We know that \vec{\tau }=\vec{r}\times\vec{f}

 \vec{r}.\vec{\tau }=\vec{r}.\left ( \vec{r}\times \vec{f} \right )=0

\therefore \vec{f}.\vec{\tau}=\vec{f}.\left ( \vec{r}\times\vec{f} \right )=0


Option 1)

\vec{r}\cdot \vec{T}= 0\: \: and\: \: \vec{F}\cdot \vec{T}\neq 0

This is an incorrect option.

Option 2)

\vec{r}\cdot \vec{T} \neq0\: \: and\: \: \vec{F}\cdot \vec{T} = 0

This is an incorrect option.

Option 3)

\vec{r}\cdot \vec{T} \neq0\: \: and\: \: \vec{F}\cdot \vec{T} \neq 0

This is an incorrect option.

Option 4)

\vec{r}\cdot \vec{T} = 0\: \: and\: \: \vec{F}\cdot \vec{T} = 0

This is the correct option.

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Aadil

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