A man has mass 70 kg and the mass of his wife is 50 kg. The ratio of the inertia of the man to the inertia of his wife is

Options

A. ` 5 : 7 `
B. ` 1 : 2 `
C. ` 7 : 5 `
D. ` 1 : 3 `

Explanation

To solve the problem, we need to find the ratio of the inertia of the man to the inertia of his wife. Inertia is directly proportional to mass, which means that the mass of an object determines its inertia.

### Step-by-Step Solution:

1. **Identify the Masses**:
- Mass of the man (M_man) = 70 kg
- Mass of the wife (M_wife) = 50 kg

2. **Understand the Concept of Inertia**:
- Inertia is a property of matter that quantifies its resistance to changes in motion. The greater the mass of an object, the greater its inertia.

3. **Set Up the Ratio**:
- The ratio of the inertia of the man to the inertia of his wife can be expressed as:
\[ \text{Ratio} = \frac{M_{\text{man}}}{M_{\text{wife}}} \]

4. **Substitute the Values**:
- Substitute the masses into the ratio:
\[ \text{Ratio} = \frac{70 \text{ kg}}{50 \text{ kg}} \]

5. **Simplify the Ratio**:
- To simplify the ratio, divide both the numerator and the denominator by 10:
\[ \text{Ratio} = \frac{7}{5} \]

6. **Final Answer**:
- Therefore, the ratio of the inertia of the man to the inertia of his wife is:
\[ \text{Ratio} = 7 : 5 \]