
Assertion: Vector product of two vectors is an axial vector.
Reason: If $\vec{v}$= instantaneous velocity , $\vec{r}$= radius vector and $\vec{w}$= angular velocity , then $\vec{w}=\vec{v}\times \vec{r}$
A. Both assertion and reason are correct and reason is the correct explanation for assertion
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.
Answer
233.1k+ views
Hint: First we have to know what an axial vector is. Axial vectors are those functions along the axis of rotation and show the rotational influence. Odd number of cross products gives axial vectors while even numbers give normal vectors. With the help of definition, we find out the correct option.
Complete step by step solution:
We know axial vector is a vector that does not change its sign on changing the coordinate system to a new system by a reflection in the origin. When the direction of the coordinate axes are inverted, the sign will remain the same as the cross product of two vectors. Hence the cross product of two vectors will be an axial vector.
Now let $\vec{v}$= instantaneous velocity , $\vec{r}$= radius vector and $\vec{w}$= angular velocity. Consider a circular disc rotating about its axis with angular velocity w. A particle at a distance r from axis, whose position vector is r, is moving at a speed
$v=\dfrac{2\pi r}{T}$
Where, T = period of rotation = time taken to go round once =$\dfrac{2\pi }{w}$
So v = $\dfrac{2\pi r }{\dfrac{2\pi }{w}}= w\,r$
That is the particle moving with speed = wr and its direction is tangential which is the same as $w\times r$ (vector product ). If origin of coordinate system is not at centre, but at some distance on the axis then,
$v=wr\sin \theta $
That is $\vec{v}=\vec{w}\times \vec{r}$
Thus, the assertion is correct but the reason is incorrect.
Hence, option C is correct.
Note: We should take care about the fact that an axial vector is present when the object is in circular motion, and we are not able to find the axial vector in linear motion.
Complete step by step solution:
We know axial vector is a vector that does not change its sign on changing the coordinate system to a new system by a reflection in the origin. When the direction of the coordinate axes are inverted, the sign will remain the same as the cross product of two vectors. Hence the cross product of two vectors will be an axial vector.
Now let $\vec{v}$= instantaneous velocity , $\vec{r}$= radius vector and $\vec{w}$= angular velocity. Consider a circular disc rotating about its axis with angular velocity w. A particle at a distance r from axis, whose position vector is r, is moving at a speed
$v=\dfrac{2\pi r}{T}$
Where, T = period of rotation = time taken to go round once =$\dfrac{2\pi }{w}$
So v = $\dfrac{2\pi r }{\dfrac{2\pi }{w}}= w\,r$
That is the particle moving with speed = wr and its direction is tangential which is the same as $w\times r$ (vector product ). If origin of coordinate system is not at centre, but at some distance on the axis then,
$v=wr\sin \theta $
That is $\vec{v}=\vec{w}\times \vec{r}$
Thus, the assertion is correct but the reason is incorrect.
Hence, option C is correct.
Note: We should take care about the fact that an axial vector is present when the object is in circular motion, and we are not able to find the axial vector in linear motion.
Recently Updated Pages
JEE Main 2023 April 6 Shift 1 Question Paper with Answer Key

JEE Main 2023 April 6 Shift 2 Question Paper with Answer Key

JEE Main 2023 (January 31 Evening Shift) Question Paper with Solutions [PDF]

JEE Main 2023 January 30 Shift 2 Question Paper with Answer Key

JEE Main 2023 January 25 Shift 1 Question Paper with Answer Key

JEE Main 2023 January 24 Shift 2 Question Paper with Answer Key

Trending doubts
JEE Main 2026: Session 2 Registration Open, City Intimation Slip, Exam Dates, Syllabus & Eligibility

JEE Main 2026 Application Login: Direct Link, Registration, Form Fill, and Steps

JEE Main Marking Scheme 2026- Paper-Wise Marks Distribution and Negative Marking Details

Understanding the Angle of Deviation in a Prism

Hybridisation in Chemistry – Concept, Types & Applications

How to Convert a Galvanometer into an Ammeter or Voltmeter

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Laws of Motion Class 11 Physics Chapter 4 CBSE Notes - 2025-26

Waves Class 11 Physics Chapter 14 CBSE Notes - 2025-26

Mechanical Properties of Fluids Class 11 Physics Chapter 9 CBSE Notes - 2025-26

Thermodynamics Class 11 Physics Chapter 11 CBSE Notes - 2025-26

Units And Measurements Class 11 Physics Chapter 1 CBSE Notes - 2025-26

