An solid cylinder of mass `20 kg` and radius `20 cm` rotates about its axis with a angular speed `100 rad s^-1`. The angular momentum of the cylinder about its axis is: a) 40 J s b) 400 J s c) 20 J s d) 200 J s

Options

A. 40 J s
B. 400 J s
C. 20 J s
D. 200 J s

Explanation

To find the angular momentum of a solid cylinder rotating about its axis, we can follow these steps:

### Step 1: Identify the given values
- Mass of the cylinder, \( m = 20 \, \text{kg} \)
- Radius of the cylinder, \( r = 20 \, \text{cm} = 0.2 \, \text{m} \) (convert cm to m)
- Angular speed, \( \omega = 100 \, \text{rad/s} \)

### Step 2: Calculate the moment of inertia \( I \)
The moment of inertia \( I \) for a solid cylinder rotating about its axis is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
Substituting the values:
\[ I = \frac{1}{2} \times 20 \, \text{kg} \times (0.2 \, \text{m})^2 \]
Calculating \( (0.2 \, \text{m})^2 \):
\[ (0.2)^2 = 0.04 \, \text{m}^2 \]
Now substituting this back into the equation for \( I \):
\[ I = \frac{1}{2} \times 20 \times 0.04 = \frac{20 \times 0.04}{2} = \frac{0.8}{2} = 0.4 \, \text{kg m}^2 \]

### Step 3: Calculate the angular momentum \( L \)
The angular momentum \( L \) is given by the formula:
\[ L = I \omega \]
Substituting the values of \( I \) and \( \omega \):
\[ L = 0.4 \, \text{kg m}^2 \times 100 \, \text{rad/s} \]
Calculating this gives:
\[ L = 40 \, \text{kg m}^2/\text{s} = 40 \, \text{J s} \]

### Final Answer
The angular momentum of the cylinder about its axis is:
\[ \boxed{40 \, \text{J s}} \]