Least count of a vernier callipers is `0.01 cm` When the two jaws of the instrument touch each other the `5th` division of the vernier scale coincide with a main scale division and the zero of the vernier scale lies to the left of the zero of the main scale. Furthermore while measuring the diameter of a sphere, the zero markof the vernier scale lies between `2.4 cm` and `2.5 cm` and the `6th` vernier division coincides with a main scale division. Calculate the diameter of the sphere.

Explanation

To calculate the diameter of the sphere using the given Vernier caliper readings, we will follow these steps:

### Step 1: Identify the least count and the zero error
The least count of the Vernier caliper is given as \(0.01 \, \text{cm}\).

### Step 2: Determine the zero error
The problem states that when the jaws of the instrument touch, the 5th division of the Vernier scale coincides with a main scale division, and the zero of the Vernier scale lies to the left of the zero of the main scale. This indicates a negative zero error.

To calculate the negative zero error:
\[ \text{Negative Zero Error} = \text{Coinciding division} \times \text{Least Count} = 5 \times 0.01 \, \text{cm} = 0.05 \, \text{cm} \]

### Step 3: Measure the diameter of the sphere
While measuring the diameter, the zero mark of the Vernier scale lies between \(2.4 \, \text{cm}\) and \(2.5 \, \text{cm}\). We take the lower value, which is \(2.4 \, \text{cm}\). The 6th division of the Vernier scale coincides with a main scale division.

### Step 4: Calculate the reading from the Vernier scale
The reading from the Vernier scale can be calculated as follows:
\[ \text{Vernier Scale Reading} = \text{Coinciding Division} \times \text{Least Count} = 6 \times 0.01 \, \text{cm} = 0.06 \, \text{cm} \]

### Step 5: Calculate the final diameter of the sphere
Now we can calculate the diameter \(D\) of the sphere using the formula:
\[ D = \text{Main Scale Reading} + \text{Vernier Scale Reading} + \text{Negative Zero Error} \]
Substituting the values we have:
\[ D = 2.4 \, \text{cm} + 0.06 \, \text{cm} + 0.05 \, \text{cm} \]
\[ D = 2.4 \, \text{cm} + 0.11 \, \text{cm} = 2.51 \, \text{cm} \]

### Final Answer:
The diameter of the sphere is \(2.51 \, \text{cm}\).

---