Question

Where will the hour of clock stop if it starts from 8 and turns through 2 right angles?

Answer 1

Hint: Here two right angles means that the total angle of \[180\] degrees. We know that the total angle in a circle is 360 degrees and the angle moved for one hour can be calculated as \[\dfrac{360}{12}={{30}^{0}}\]. Here, we divided 360 degrees by 12 because in a clock there will 12 hours. Now, we take 2 right angles worth of hours, that is, if for one hour it is 30 degrees then for how many hours it will take 180 degrees then we get the required to answer by adding that many hours to the initial position of hour’s hand.

Complete step-by-step solution
First let us find that for each hour how much degrees that a hand in a clock should move by using the following formula
\[\text{angle for each part = }\dfrac{360}{\text{total number of parts}}\]
We know that in a clock there will be 12 hours. So, the total number of parts will be 12. By substituting that in above formula we get
\[\begin{align}
  & \Rightarrow \text{angle for each part = }\dfrac{360}{12} \\
 & \Rightarrow \text{angle for each part = 3}{{\text{0}}^{0}} \\
\end{align}\]
Now, let us calculate how many hours it will take to complete 2 right angles that is 180 degrees by using following formula
\[\Rightarrow \text{number of hours = }\dfrac{\text{angle need to be completed}}{\text{angle takes to complete one hour}}\]
By substituting the values of angle need to be completed as 180 degrees and angle takes to complete one hour as 30 degrees in the above formula we get
\[\begin{align}
  & \Rightarrow \text{number of hours = }\dfrac{180}{30} \\
 & \Rightarrow \text{number of hours = 6} \\
\end{align}\]
So, it will take 6 hours to complete 2 right angles in a clock by the hour’s hand.
We know that initially, the hour’s hand is at the position of 8 we will add 6 hours to it in order to get the final position after completing 2 right angles.
By adding 6 hours to 8 we get
\[\Rightarrow 8+6=14\]
We know that in a clock after the value of 12 it again starts from 1. So 14 in the clock represents 2 in the clock.
So the clock will stop at 2 after completing 2 right angles in the clock by hour’s hand.

Note: Some students will leave the answer at 14 in the above solution at this point.
\[\Rightarrow 8+6=14\]
You need to convert into the number in the clock because we are dealing with the position of the hour’s hand in the clock. So, the answer should be 2.