The radius of of disc is 2 m the radius of gyration of disc about an axis passing through its diameter is

Options

A. 2 m
B. 2 cm
C. 1 m
D. 0.2 m

Explanation

To find the radius of gyration of a disc about an axis passing through its diameter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- The radius of the disc (r) = 2 m.

2. **Understand the Concept of Radius of Gyration:**
- The radius of gyration (k) is related to the moment of inertia (I) of the object. It is defined by the equation:
\[ I = m \cdot k^2 \]
where \( m \) is the mass of the disc.

3. **Calculate the Moment of Inertia of the Disc:**
- The moment of inertia of a disc about an axis passing through its diameter is given by:
\[ I = \frac{1}{4} m r^2 \]

4. **Set Up the Equation Using the Radius of Gyration:**
- From the definition of the radius of gyration, we can equate the two expressions for moment of inertia:
\[ \frac{1}{4} m r^2 = m k^2 \]

5. **Cancel the Mass (m) from Both Sides:**
- Since mass \( m \) appears on both sides of the equation, we can cancel it out:
\[ \frac{1}{4} r^2 = k^2 \]

6. **Solve for the Radius of Gyration (k):**
- Taking the square root of both sides gives:
\[ k = \sqrt{\frac{1}{4} r^2} = \frac{r}{2} \]

7. **Substitute the Value of r:**
- Now substitute the value of the radius \( r = 2 \) m into the equation:
\[ k = \frac{2}{2} = 1 \text{ m} \]

8. **Conclusion:**
- The radius of gyration of the disc about an axis passing through its diameter is:
\[ k = 1 \text{ m} \]

### Final Answer:
The radius of gyration of the disc is **1 meter**.

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