The ratio of gravitational mass to inertial mass is equal to:

Options

A. `(1)/(2)`
B. 2
C. 1
D. None of these

Explanation

To solve the question regarding the ratio of gravitational mass to inertial mass, we can follow these steps:

### Step 1: Understand the Definitions
- **Gravitational Mass**: This is the mass that determines the strength of the gravitational force experienced by an object in a gravitational field. It is measured by the weight of the object.
- **Inertial Mass**: This is the mass that determines the resistance of an object to any force applied to it. It is measured by the object's acceleration when a force is applied.

### Step 2: Establish the Relationship
- According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Here, 'm' represents the inertial mass.
- The gravitational force acting on an object is given by the equation F = mg, where 'g' is the acceleration due to gravity, and 'm' represents the gravitational mass.

### Step 3: Set Up the Ratio
- To find the ratio of gravitational mass (m_g) to inertial mass (m_i), we can express it as:
\[ \text{Ratio} = \frac{m_g}{m_i} \]

### Step 4: Use the Equivalence Principle
- According to the equivalence principle, gravitational mass and inertial mass are equivalent. Therefore, we can say:
\[ m_g = m_i \]

### Step 5: Calculate the Ratio
- Substituting the equivalence into the ratio gives us:
\[ \text{Ratio} = \frac{m_g}{m_i} = \frac{m_i}{m_i} = 1 \]

### Conclusion
- Thus, the ratio of gravitational mass to inertial mass is equal to 1.

### Final Answer
- The ratio of gravitational mass to inertial mass is **1**.

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