Percentage error in measuring the radius and mass of a solid sphere are 3 % & 1 % respectively. The error in measurement of moment of inertia about to its diameter is :-

Explanation

To solve the problem of finding the error in the measurement of the moment of inertia of a solid sphere about its diameter, we will follow these steps:

### Step 1: Understand the formula for moment of inertia
The moment of inertia (I) of a solid sphere about its diameter is given by the formula:
\[ I = \frac{2}{5} m r^2 \]
where \( m \) is the mass of the sphere and \( r \) is the radius.

### Step 2: Identify the percentage errors
We are given:
- Percentage error in measuring the radius (\( r \)) = 3%
- Percentage error in measuring the mass (\( m \)) = 1%

### Step 3: Relate the errors to the moment of inertia
To find the percentage error in the moment of inertia, we need to differentiate the moment of inertia formula with respect to its variables. The percentage error in a product or power can be calculated using the following relation:
\[ \text{Percentage error in } I = \text{Percentage error in } m + 2 \times \text{Percentage error in } r \]
Here, the factor of 2 comes from the fact that the radius is squared in the moment of inertia formula.

### Step 4: Substitute the values
Now we can substitute the known percentage errors into the formula:
\[ \text{Percentage error in } I = 1\% + 2 \times 3\% \]

### Step 5: Calculate the total percentage error
Calculating this gives:
\[ \text{Percentage error in } I = 1\% + 6\% = 7\% \]

### Final Answer
The percentage error in the measurement of the moment of inertia about its diameter is **7%**.

---