Where will the hand of a clock stop if it
starts at 5 and makes `(3)/(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 \( \frac{3}{4} \) of a revolution clockwise, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Clock Positions**:
A clock has 12 positions, numbered from 1 to 12. Starting from 12 and moving clockwise, the positions are:
- 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

2. **Identify the Starting Point**:
The hand starts at the position 5.

3. **Determine the Total Degrees in a Revolution**:
A complete revolution around the clock is 360 degrees.

4. **Calculate the Degrees for \( \frac{3}{4} \) of a Revolution**:
To find \( \frac{3}{4} \) of a revolution, we calculate:
\[ \frac{3}{4} \times 360 = 270 \text{ degrees} \]

5. **Determine the Movement in Terms of Hour Positions**:
Since each hour on the clock represents 30 degrees (because \( 360 \div 12 = 30 \)), we can find how many hour positions the hand will move:
\[ \frac{270}{30} = 9 \text{ hour positions} \]

6. **Count the Hour Positions from 5**:
Starting from 5 and moving 9 hour positions clockwise:
- 5 to 6 (1)
- 6 to 7 (2)
- 7 to 8 (3)
- 8 to 9 (4)
- 9 to 10 (5)
- 10 to 11 (6)
- 11 to 12 (7)
- 12 to 1 (8)
- 1 to 2 (9)

After moving 9 positions, the hand will stop at 2.

7. **Final Answer**:
Therefore, the hand of the clock will stop at 2 after making \( \frac{3}{4} \) of a revolution clockwise from 5.