A cylinder of 500 g and radius 10 cm has moment of inertia about an axis passing through its centre and parallel to its length is

Options

A. `2.5xx10^(-3)kg m^(2)`
B. `2xx10^(-3)kg m^(2)`
C. `5xx10^(-3)kg m^(2)`
D. `3.5xx10^(-3)kg m^(2)`

Explanation

To find the moment of inertia of a cylinder about an axis passing through its center and parallel to its length, we can use the formula for the moment of inertia of a solid cylinder:

\[ I = \frac{1}{2} m r^2 \]

where:
- \( I \) is the moment of inertia,
- \( m \) is the mass of the cylinder,
- \( r \) is the radius of the cylinder.

### Step 1: Convert the mass from grams to kilograms
Given:
- Mass \( m = 500 \) grams

To convert grams to kilograms, we divide by 1000:

\[ m = \frac{500}{1000} = 0.5 \, \text{kg} \]

### Step 2: Convert the radius from centimeters to meters
Given:
- Radius \( r = 10 \) cm

To convert centimeters to meters, we divide by 100:

\[ r = \frac{10}{100} = 0.1 \, \text{m} \]

### Step 3: Substitute the values into the moment of inertia formula
Now we can substitute the values of \( m \) and \( r \) into the moment of inertia formula:

\[ I = \frac{1}{2} m r^2 \]

Substituting the values:

\[ I = \frac{1}{2} \times 0.5 \times (0.1)^2 \]

### Step 4: Calculate \( r^2 \)
Calculating \( r^2 \):

\[ r^2 = (0.1)^2 = 0.01 \]

### Step 5: Calculate the moment of inertia
Now substituting \( r^2 \) back into the formula:

\[ I = \frac{1}{2} \times 0.5 \times 0.01 \]

Calculating this:

\[ I = \frac{1}{2} \times 0.5 \times 0.01 = 0.0025 \, \text{kg m}^2 \]

### Final Answer
The moment of inertia of the cylinder is:

\[ I = 0.0025 \, \text{kg m}^2 \]