Assertion: Value of radius of gyration of a body depends on axis of rotation.
Reason: Radius of gyration is root mean square distance of particle of the body from the axis of rotation.

Options

A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion
C. Assertion is true but reason is false.
D. Both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason given.

### Step 1: Understand the Assertion
The assertion states that "the value of the radius of gyration of a body depends on the axis of rotation."

**Explanation**: The radius of gyration (k) is defined as the distance from the axis of rotation at which the entire mass of the body can be assumed to be concentrated for the purpose of calculating its moment of inertia (I). The formula for the radius of gyration is given by:

\[ k = \sqrt{\frac{I}{m}} \]

where \(I\) is the moment of inertia and \(m\) is the total mass of the body. Since the moment of inertia depends on the distribution of mass relative to the axis of rotation, it follows that the radius of gyration also depends on the axis of rotation.

### Step 2: Understand the Reason
The reason states that "the radius of gyration is the root mean square distance of particles of the body from the axis of rotation."

**Explanation**: The radius of gyration can indeed be interpreted as the root mean square (RMS) distance of the mass elements from the axis of rotation. The moment of inertia for a system of particles is given by:

\[ I = \sum m_i r_i^2 \]

where \(m_i\) is the mass of each particle and \(r_i\) is its distance from the axis of rotation. The radius of gyration can be expressed in terms of these distances as:

\[ k = \sqrt{\frac{\sum m_i r_i^2}{M}} \]

where \(M\) is the total mass of the system. This shows that \(k\) is indeed related to the distances of the particles from the axis of rotation.

### Step 3: Conclusion
Both the assertion and reason are true. Furthermore, the reason correctly explains the assertion because the dependence of the radius of gyration on the axis of rotation is rooted in its definition as the root mean square distance of the mass distribution from that axis.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

---