To solve the given problem, we need to analyze both statements and determine their validity. Let's break it down step by step.
### Step 1: Understanding Statement 1
**Statement 1:** If a particle is projected from the ground with some velocity (not very large) at an angle with the horizontal, the path of the particle is assumed to be parabolic, although it is not exactly parabolic.
**Explanation:**
When a particle is projected at an angle, it follows a curved trajectory due to the influence of gravity. In ideal projectile motion, where air resistance is negligible and gravity is constant, the path is a perfect parabola. However, in reality, factors like air resistance and the variation of gravitational acceleration can cause deviations from a perfect parabolic path. For small velocities (not very large), the assumption of a parabolic path holds reasonably well.
### Step 2: Understanding Statement 2
**Statement 2:** The magnitude of acceleration due to gravity at all places is assumed to be constant, although it is not so.
**Explanation:**
The acceleration due to gravity (g) is given by the formula \( g = \frac{GM}{r^2} \), where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth. Since the Earth is not a perfect sphere and its density varies, the value of g changes slightly depending on the location (altitude, latitude, etc.). However, for simplicity in calculations, we often assume g to be constant (approximately 9.81 m/s²) for small heights and distances.
### Step 3: Validating the Statements
- **Validity of Statement 1:** The statement is correct because, while the path is assumed to be parabolic, real-world factors can cause deviations.
- **Validity of Statement 2:** This statement is also correct as it accurately describes the variation of g due to the Earth's shape and density.
### Step 4: Conclusion
Both statements are true, and Statement 2 provides a correct explanation for Statement 1.
### Final Answer:
- **Statement 1:** True
- **Statement 2:** True
- **Explanation:** Statement 2 explains why the path of the projectile is assumed to be parabolic despite the variations in gravitational acceleration.
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