Let F⃗ be the force acting on a particle having position vector r⃗, and τ⃗ be the torque of this

Name: Problem 63, Chapter 6: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T07:19:08-08:00
Duration: 1 min 31 s
Channel: Arpit Gupta
Description: Let F⃗ be the force acting on a particle having position vector r⃗, and τ⃗ be the torque of this force about the origin. Then [2 0 0 3] (A) r⃗ ·T⃗=0 and F⃗ ·τ⃗ ≠0 (B) r⃗ ·T⃗ ≠0 and F⃗ ·τ⃗=0 (C) r⃗ ·F⃗ ≠0 and F⃗ ·τ⃗ ≠0 (D) r⃗ ·τ⃗=0 F⃗ ·τ⃗=0

step 1 we have to find the value of force and torque here. So now let's see the solution. First of all,

Question

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$, and $\vec{\tau}$ be the torque of this force about the origin. Then $[\mathbf{2 0 0 3}]$ (A) $\vec{r} \cdot \vec{T}=0$ and $\vec{F} \cdot \vec{\tau} \neq 0$ (B) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{\tau}=0$ (C) $\vec{r} \cdot \vec{F} \neq 0$ and $\vec{F} \cdot \vec{\tau} \neq 0$ (D) $\vec{r} \cdot \vec{\tau}=0 \vec{F} \cdot \vec{\tau}=0$

   Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$, and $\vec{\tau}$ be the torque of this force about the origin. Then $[\mathbf{2 0 0 3}]$
(A) $\vec{r} \cdot \vec{T}=0$ and $\vec{F} \cdot \vec{\tau} \neq 0$
(B) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{\tau}=0$
(C) $\vec{r} \cdot \vec{F} \neq 0$ and $\vec{F} \cdot \vec{\tau} \neq 0$
(D) $\vec{r} \cdot \vec{\tau}=0 \vec{F} \cdot \vec{\tau}=0$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 6, Problem 63

Instant Answer

Solved by Expert Arpit Gupta

10/06/2021

Step 1

e., $\vec{\tau} = \vec{r} \times \vec{F}$. Show more…

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Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$, and $\vec{\tau}$ be the torque of this force about the origin. Then $[\mathbf{2 0 0 3}]$ (A) $\vec{r} \cdot \vec{T}=0$ and $\vec{F} \cdot \vec{\tau} \neq 0$ (B) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{\tau}=0$ (C) $\vec{r} \cdot \vec{F} \neq 0$ and $\vec{F} \cdot \vec{\tau} \neq 0$ (D) $\vec{r} \cdot \vec{\tau}=0 \vec{F} \cdot \vec{\tau}=0$

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Key Concepts

Dot Product and Orthogonality

The dot product measures the magnitude of one vector in the direction of another. When two vectors are perpendicular, their dot product is zero, a fact that underlies the result that the torque vector is orthogonal to both the position and force vectors.

Torque

Torque quantifies the tendency of a force to cause rotational motion about an axis. It is computed as the cross product of the position vector and the force vector, capturing both the magnitude of the force and its lever arm relative to the pivot point.

Cross Product

The cross product of two vectors yields a third vector that is perpendicular to the plane formed by the original vectors. This property is crucial in determining that the torque vector is orthogonal to both the position and force vectors.

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