
Assertion: Angle and angular displacement are dimensionless quantities.
Reason: Angle is equal to arc length divided by radius.
(A) Both Assertion and Reason are correct and Reason is the correct explanation for the assertion.
(B) Both Assertion and Reason are correct and Reason is not the correct explanation for the assertion
(C) Assertion is correct but Reason is incorrect.
(D) Both Assertion and Reason are incorrect
Answer
140.1k+ views
Hint: This could be simply solved by understanding both assertion and reason. The formula for angular displacement will help here to get the solution.
Formula used: Here, we will use the basic formula of speed, distance and time:
$\theta = \dfrac{L}{r}$
Here, $\theta $ is the angular displacement
$L$ is the arc length
$r$ is the radius.
Complete step by step answer:
We will start by considering the formula written above:
$\theta = \dfrac{L}{r}$
$\theta = \dfrac{L}{r} = \dfrac{{\left[ L \right]}}{{\left[ L \right]}} = \operatorname{dimensionless} $
So, both the statements are proving correct.
But verification of one statement does not justify the other statement.
So, Both Assertion and Reason are correct and Reason is not the correct explanation for the assertion
Thus, the correct option is B.
Additional Information: Angular displacement is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path. Angular displacement is measured in units of radians. Two pi radians equal 360 degrees. The angular displacement is not a length (not measured in meters or feet), so an angular displacement is different from a linear displacement. Angular displacement is a vector quantity and the angle subtended by any point of the rotating body with its axis. In S.I. its unit is radian. Angular velocity is the rate of change of angular displacement and it is also a vector quantity. Also, Displacement can be negative because it defines a change in position of an object while carefully monitoring its direction.
Note: The general mistake made here is in assuming that the reason is always the correct explanation of the assertion which does not hold true always. So we need to keep it in mind before we select the correct answer.
Formula used: Here, we will use the basic formula of speed, distance and time:
$\theta = \dfrac{L}{r}$
Here, $\theta $ is the angular displacement
$L$ is the arc length
$r$ is the radius.
Complete step by step answer:
We will start by considering the formula written above:
$\theta = \dfrac{L}{r}$
$\theta = \dfrac{L}{r} = \dfrac{{\left[ L \right]}}{{\left[ L \right]}} = \operatorname{dimensionless} $
So, both the statements are proving correct.
But verification of one statement does not justify the other statement.
So, Both Assertion and Reason are correct and Reason is not the correct explanation for the assertion
Thus, the correct option is B.
Additional Information: Angular displacement is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path. Angular displacement is measured in units of radians. Two pi radians equal 360 degrees. The angular displacement is not a length (not measured in meters or feet), so an angular displacement is different from a linear displacement. Angular displacement is a vector quantity and the angle subtended by any point of the rotating body with its axis. In S.I. its unit is radian. Angular velocity is the rate of change of angular displacement and it is also a vector quantity. Also, Displacement can be negative because it defines a change in position of an object while carefully monitoring its direction.
Note: The general mistake made here is in assuming that the reason is always the correct explanation of the assertion which does not hold true always. So we need to keep it in mind before we select the correct answer.
Recently Updated Pages
Difference Between Circuit Switching and Packet Switching

Difference Between Mass and Weight

JEE Main Participating Colleges 2024 - A Complete List of Top Colleges

JEE Main Maths Paper Pattern 2025 – Marking, Sections & Tips

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main 2025 Helpline Numbers - Center Contact, Phone Number, Address

Trending doubts
JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Physics Average Value and RMS Value JEE Main 2025

Charging and Discharging of Capacitor

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Collision - Important Concepts and Tips for JEE

Displacement-Time Graph and Velocity-Time Graph for JEE

Other Pages
NCERT Solutions for Class 11 Physics Chapter 7 Gravitation

NCERT Solutions for Class 11 Physics Chapter 3 Motion In A Plane

NCERT Solutions for Class 11 Physics Chapter 14 Waves

A spherical ball of mass 20kg is stationary at the class 11 physics JEE_Main

A water pump of 1 horse power is required to flow water class 11 physics JEE_Main

JEE Advanced 2025 Revision Notes for Physics on Modern Physics
