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Question: In 30 minutes, the hours hand of a clock turns through 1.\[\dfrac{\pi }{6}\]radians 2.\[\dfrac{\...

In 30 minutes, the hours hand of a clock turns through
1.π6\dfrac{\pi }{6}radians
2.π12\dfrac{\pi }{{12}} radians
3.π24\dfrac{\pi }{{24}} radians
4.π\pi radians

Explanation

Solution

As we know that hours hand complete it’s one rotation in 12{\text{12}} hours and in 12{\text{12}}hours in turns about 2π{{2\pi }}angle so rotation per hour can be given as 2π12\dfrac{{{{2\pi }}}}{{12}}radians. As now compared with this proceed for the given question.

Complete step-by-step answer:
As given that in 3030minutes we have to calculate hours hand rotation.
As we know that hours hand complete it’s one rotation in 12{\text{12}} hours and in 12{\text{12}}hours in turns about 2π{{2\pi }}angle so rotation per hour can be given as 2π12\dfrac{{{{2\pi }}}}{{12}}radians (in 6060minutes).
So in 3030minutes is,

 = (12)2π12  = π12  {\text{ = (}}\dfrac{{\text{1}}}{{\text{2}}}{\text{)}}\dfrac{{{{2\pi }}}}{{{\text{12}}}} \\\ {\text{ = }}\dfrac{{{\pi }}}{{{\text{12}}}} \\\

Hence, option (B) is our required answer.

Note: Radian describes the plane angle subtended by a circular arc, as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle.
The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends. One radian is just under 57.3{\text{57}}{\text{.3}}degrees.