A spherometer has 250 equal divisions marked along the periphery of its disc, and one full rotation of the disadvances by 0.0625 cm on the main scale. What is the least count of the spherometer ?

Explanation

To find the least count of the spherometer, we can follow these steps:

### Step 1: Understand the given data
We are given:
- The number of equal divisions on the periphery of the disc = 250
- The distance advanced by one full rotation of the disc = 0.0625 cm

### Step 2: Use the formula for least count
The least count (LC) of an instrument can be calculated using the formula:
\[ \text{Least Count} = \frac{\text{Value of one complete rotation}}{\text{Number of divisions}} \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \text{Least Count} = \frac{0.0625 \, \text{cm}}{250} \]

### Step 4: Perform the division
Now, we perform the division:
\[ \text{Least Count} = \frac{0.0625}{250} \]

To simplify this, we can convert 0.0625 into a fraction:
\[ 0.0625 = \frac{625}{10000} \]
Now we can rewrite the least count:
\[ \text{Least Count} = \frac{625/10000}{250} = \frac{625}{10000 \times 250} \]

Calculating \(10000 \times 250\):
\[ 10000 \times 250 = 2500000 \]
Thus, we have:
\[ \text{Least Count} = \frac{625}{2500000} \]

### Step 5: Simplify the fraction
Now we simplify the fraction:
\[ 625 \div 625 = 1 \quad \text{and} \quad 2500000 \div 625 = 4000 \]
So,
\[ \text{Least Count} = \frac{1}{4000} \, \text{cm} \]

### Step 6: Convert to scientific notation
Finally, we can express this in scientific notation:
\[ \text{Least Count} = 2.5 \times 10^{-4} \, \text{cm} \]

### Final Answer
The least count of the spherometer is:
\[ \text{Least Count} = 2.5 \times 10^{-4} \, \text{cm} \]

---