Question

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 1

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.