Where will the hand of a clock stop if it
starts at 5 and makes `(1)/(4)` of a revolution, clockwise ?

Answer

To solve the problem of where the hand of a clock will stop if it starts at 5 and makes \( \frac{1}{4} \) of a revolution clockwise, we can follow these steps:

### Step 1: Understand the Clock Positions
A clock has 12 positions, each representing an hour. The positions are:
- 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

### Step 2: Determine the Starting Position
The hand starts at the 5 o'clock position.

### Step 3: Calculate the Degrees of a Full Revolution
A full revolution of the clock is 360 degrees. Therefore, \( \frac{1}{4} \) of a revolution is calculated as follows:
\[ \frac{1}{4} \times 360 = 90 \text{ degrees} \]

### Step 4: Identify the Movement of the Clock Hand
Since the clock hand moves clockwise, we need to determine how many hour positions correspond to a movement of 90 degrees. Each hour position on the clock represents \( \frac{360}{12} = 30 \) degrees.

### Step 5: Calculate the Number of Hour Positions Moved
Now, we can find out how many hour positions the hand moves by dividing the degrees moved by the degrees per hour position:
\[ \frac{90 \text{ degrees}}{30 \text{ degrees/hour}} = 3 \text{ hour positions} \]

### Step 6: Determine the Final Position
Starting from 5, we move 3 positions clockwise:
- From 5 to 6 (1 position)
- From 6 to 7 (2 positions)
- From 7 to 8 (3 positions)

Thus, the hand will stop at the 8 o'clock position.

### Final Answer
The hand of the clock will stop at 8.

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