Which of the following are incorrect statements about acceleration due to gravity ?

Options

A. it is independent of mass, shape, size ect of falling body
B. It is a universal constant and does not depend on place, position and planet
C. It depends only on mass of the central body
D. Near the earth surface its value is `9.8 m//s^(2)`

Answer

To determine which statements about acceleration due to gravity are incorrect, we need to analyze the nature of gravitational acceleration and its dependence on various factors. Let's break down the problem step by step.

### Step 1: Understanding Acceleration Due to Gravity
The acceleration due to gravity (g) is defined as the acceleration experienced by an object due to the gravitational force exerted by a massive body, such as a planet. The formula for gravitational acceleration at a distance r from the center of a planet with mass M is given by:

\[ g = \frac{GM}{r^2} \]

Where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( r \) is the distance from the center of the planet.

### Step 2: Analyzing the Statements
Now, let's analyze the provided statements one by one:

1. **Statement 1**: "It is independent of mass, shape, size, etc. of the free-falling body."
- This statement is **incorrect**. The acceleration due to gravity is indeed independent of the mass, shape, or size of the falling body. However, it does depend on the mass of the planet and the distance from its center.

2. **Statement 2**: "It is a universal constant and does not depend on the position and planet; it depends only on mass and central body."
- This statement is **incorrect**. While \( g \) is a constant near the Earth's surface (approximately 9.8 m/s²), it varies with altitude and is different for different planets. Thus, it does depend on the position and the planet.

3. **Statement 3**: "It depends on the mass of the central body."
- This statement is **correct**. The acceleration due to gravity is directly proportional to the mass of the planet (central body) and inversely proportional to the square of the radius.

### Step 3: Conclusion
From the analysis, we find that the incorrect statements about acceleration due to gravity are:

- **Statement 1**: Incorrect (it is independent of the free-falling body's mass, shape, etc.)
- **Statement 2**: Incorrect (it does depend on the position and the planet)

Thus, the answer to the question is that Statements 1 and 2 are incorrect.