The force of freely falling body is directly proportional to

Options

A. mass of body
B. acceleration of body
C. velocity of body
D. both (a) and (b)

Explanation

To solve the question, "The force of a freely falling body is directly proportional to," we can follow these steps:

### Step 1: Understand the Concept of Force
The force acting on an object can be understood through Newton's Second Law of Motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). This can be expressed as:
\[ F = m \cdot a \]

### Step 2: Identify the Forces Acting on a Freely Falling Body
When a body is in free fall, the only force acting on it is the force of gravity. This force can be calculated using the formula:
\[ F = m \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \) on the surface of the Earth).

### Step 3: Analyze the Proportionality
From the equation \( F = m \cdot g \), we can see that the force of a freely falling body is directly proportional to its mass (m) and the acceleration due to gravity (g). Since \( g \) is a constant, the force is directly proportional to the mass of the body.

### Step 4: Consider Other Factors
The question also mentions acceleration, which in the case of free fall is equal to \( g \). Therefore, the force is also directly proportional to the acceleration of the body.

### Step 5: Eliminate Other Options
The question provides options including velocity. However, the force of a freely falling body does not depend on its velocity. Thus, we can eliminate any options that suggest a relationship with velocity.

### Conclusion
The correct answer is that the force of a freely falling body is directly proportional to both the mass of the body and the acceleration due to gravity. Therefore, the answer is:
**Both A (mass) and B (acceleration).**