Question

Unit of plane angle is ____________.
A. Radian
B. Steradian
C. Degree
D. Celsius

Answer 1

Hint: As a first step, you could define what a plane angle is. You could also provide an appropriate diagram while defining the term. Then you could recall the SI unit that is used for measuring the plane angle. Then you could also mention how to define a unit plane angle in that particular unit.

Complete solution:
Before going into the discussion about the unit of plane angle, let us understand the concept of a plane angle. It could be defined with the help of two straight lines that intersects at a particular point. The angle between these two lines is known to be a plane angle. It could be otherwise defined as the radial projection made by a line segment onto a point in a plane.

Another definition could be given to the plane angle as the ratio of arc length to the radius. That is, if $\theta$ is the plane angle, s is the arc length and r is the radius, then,
$\theta ={\displaystyle \frac{s}{r}}$.

From this expression we see that the plane angle is the ratio of two similar quantities and hence a dimensionless quantity.

The SI derived unit of plane angle is radian and is represented by ‘rad’. A radian can be defined as the plane angle that is subtended at the circle’s centre by an arc that has its length equal to the radius of the circle.

Therefore, we found that the unit of plane angle is radian. Hence, option A is the correct answer.

Note:
Another angle that is commonly used to measure plane angle is degrees. We know from the definition of unit radian that the plane angle subtended by a full circle is $\pi$ radians and when measured in degrees it is $180{}^{\circ }$. Therefore, radian to degree conversion can be done by multiplying the value in radian by, ${\displaystyle \frac{180}{\pi }}$ .