Question

How many degrees does the hour hand of a clock turn in $5$ minutes?

Answer 1

Hint: In this question we have been asked to find out how many degrees the hour hand of the clock rotates in $5$ minutes. We will calculate the required solution by first finding out how many degrees is every hour on the clock. We will then find out how much of an hour is $5$ minutes. We will then multiply both the terms to get the value of the hour hand moved in a circle. We will then divide the total degrees of a circle which is ${{360}^{\circ }}$ with the found value to get the required solution.

Complete step by step answer:
 We know that a standard clock is in the shape of a circle therefore the total degrees present on the clock is ${{360}^{\circ }}$.
We know that to complete ${{360}^{\circ }}$ of the clock total $12$ hours need to pass.
This implies that an hour is $\dfrac{1}{12}$ of a complete circle on a standard clock.
Now we know that $5$ minutes is a lesser time than an hour and since an hour contains $60$ minutes, $5$ minutes can be written as $\dfrac{5}{60}$ of an hour.
On simplifying the fraction, we get that $5$ minutes is $\dfrac{1}{12}$ of an hour.
Therefore in $5$ minutes the hour hand moves $\dfrac{1}{12}\times \dfrac{1}{12}$ of a complete circle.
On simplifying, we get that $5$ minutes makes the hour hand move $\dfrac{1}{144}$ of a complete circle.
Now since a complete circle is ${{360}^{\circ }}$, the number of degrees the hour hand moves in $5$ minutes will be:
 $\Rightarrow {{360}^{\circ }}\times \dfrac{1}{144}$
On simplifying, we get:
$\Rightarrow {{2.5}^{\circ }}$therefore, the hour hand moves ${{2.5}^{\circ }}$ in $5$ minutes.

Note: In this question we have looked at the hour hand of a clock. A clock has two other hands which are the minutes and the second’s hand. The minute hand changes its position $60$ times in an hour and the second’s hand changes its position $60$ times a minute. A standard clock is of $12$ hours and the hour hand needs to move a total of $2$ complete circles in a day which is of $24$ hours.