Two bodies A and B made of same material have the moment of inertial in the ratio `I_(A):I_(B)=16:18` The ratio of the masses `m_(A):m_(B)` is given by a) cannot be obtained b) 2:3 c) 1:1 d) 4:9

Options

A. cannot be obtained
B. `2:3`
C. `1:1`
D. `4:9`

Answer

To solve the problem, we need to find the ratio of the masses \( m_A : m_B \) given the ratio of the moments of inertia \( I_A : I_B = 16 : 18 \).

### Step-by-Step Solution:

1. **Understanding the Moment of Inertia**:
The moment of inertia \( I \) of a body is given by the formula:
\[ I = m \cdot k^2 \]
where \( m \) is the mass of the body and \( k \) is a constant that depends on the shape of the object and the axis about which it rotates.

2. **Setting Up the Ratios**:
Given the ratio of moments of inertia:
\[ \frac{I_A}{I_B} = \frac{16}{18} \]
We can express this in terms of mass and the constant \( k \):
\[ \frac{m_A \cdot k_A^2}{m_B \cdot k_B^2} = \frac{16}{18} \]

3. **Simplifying the Ratio**:
We can simplify the ratio of the moments of inertia:
\[ \frac{I_A}{I_B} = \frac{8}{9} \]
Therefore, we have:
\[ \frac{m_A \cdot k_A^2}{m_B \cdot k_B^2} = \frac{8}{9} \]

4. **Relating the Masses**:
Since both bodies are made of the same material, we can assume that the constants \( k_A \) and \( k_B \) are related to their shapes. However, without specific information about the shapes, we cannot determine \( k_A \) and \( k_B \). Thus, we cannot isolate the ratio of masses \( \frac{m_A}{m_B} \) without knowing the values of \( k_A \) and \( k_B \).

5. **Conclusion**:
Since we cannot determine the ratio of masses without additional information about the shapes of the bodies, the answer is:
\[ \text{Option A: cannot be obtained} \]