Question

Where will the hand of a clock stop if it starts at $$2$$ and makes $${\displaystyle \frac{1}{2}}$$ of a revolution, clockwise?

Answer 1

Hint: We will use the property of the clock that the hand of a clock revolves at a complete angle of $${360}^{\circ }$$which makes a complete clockwise revolution.

Complete step-by-step solution:
Step 1: To solve this problem, first we will make a clock as shown below:

In fig (1), the hand of the clock is at $$2$$. Now we know in complete clockwise revolution, the hand of the clock makes an angle of $${360}^{\circ }$$. That means the hand of the clock will start from $$2$$ and after making revolution it will again end at $$2$$.
But as per the question, the hand of the clock revolves $${\displaystyle \frac{1}{2}}$$ clockwise.
Step 2: If the hand of the clock making half revolution then the angle form by it will be half of the $${360}^{\circ }$$ as shown below:
$$\text{Angle}={\displaystyle \frac{{360}^{\circ }}{2}}\Rightarrow {180}^{\circ }$$
Step 3: Now, by drawing an angle $${180}^{\circ }$$, we can find out that the hand of the clock stops at which point as shown in the below diagram:

So, we can see from figure (2), that the hand of the clock makes an angle of $${180}^{\circ }$$ with the point $$8$$.

The hand of the clock will stop at the point $$8$$.

Note: Students should remember that the hand of the clock always revolves in the clockwise direction by making a complete revolution with an angle of $${360}^{\circ }$$.
We can also solve this question by the below method:
As we know that there are total $$12$$ symbols in the clock in which the hand of the clock revolves itself.
Now, for making a complete clockwise revolution the hand of the clock will cover all these points and will come back again at the point $$2$$.
But as per the question, it is only making half a revolution so if the hand of the clock is starting from a point $$2$$, then it will cover $$6$$ symbols in the clock which means $$2+6=8$$. So, the answer is $$8$$.