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STATEMENT -1 : In absence of air frictio...

STATEMENT -1 `:` In absence of air friction, it is claimed that all object fall with the same acceleration although, a heavier object is pulled towards the earth with more force than a lighter object.
because
STATEMENT-2 `:` Net external force is always equal to rate of change of linear momentum.

A

Statement-1 is True , Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True , Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the statements provided in the question, let's break down the reasoning step by step. ### Step-by-Step Solution: 1. **Understanding Statement 1**: - Statement 1 claims that in the absence of air friction, all objects fall with the same acceleration, even though heavier objects are pulled towards the Earth with more force than lighter objects. - This is based on the principle of gravity, where the acceleration due to gravity (g) is approximately 9.81 m/s² for all objects, regardless of their mass. 2. **Understanding Statement 2**: - Statement 2 states that the net external force is always equal to the rate of change of linear momentum. - Mathematically, this is expressed as \( F = \frac{dP}{dt} \), where \( P \) is momentum. The momentum \( P \) is defined as \( P = mv \), where \( m \) is mass and \( v \) is velocity. 3. **Applying Newton's Second Law**: - According to Newton's second law, \( F = ma \) (force equals mass times acceleration). - If we consider two objects, one heavier (mass \( m_1 \)) and one lighter (mass \( m_2 \)), both are subjected to the same gravitational acceleration \( g \). - The forces acting on them can be expressed as \( F_1 = m_1g \) and \( F_2 = m_2g \). Here, \( F_1 \) is greater than \( F_2 \) since \( m_1 > m_2 \). 4. **Relating Force, Mass, and Acceleration**: - Even though \( F_1 \) is greater than \( F_2 \), both objects experience the same acceleration \( g \) because acceleration is defined as \( a = \frac{F}{m} \). - For the heavier object: \( a = \frac{F_1}{m_1} = g \). - For the lighter object: \( a = \frac{F_2}{m_2} = g \). - Thus, both objects fall with the same acceleration despite the difference in forces acting on them. 5. **Conclusion**: - Both statements are true: Statement 1 is true because all objects fall with the same acceleration in the absence of air resistance, and Statement 2 is true as it correctly describes the relationship between force and momentum. - Furthermore, Statement 2 serves as a correct explanation for Statement 1. ### Final Answer: - **Statement 1 is true.** - **Statement 2 is true.** - **Statement 2 is the correct explanation for Statement 1.**
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