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Assertion: The centre mass of an electro...

Assertion: The centre mass of an electron and proton, when released moves faster towards proton.
Reason: Proton is heavier than electron.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given statements, we need to understand the concepts of center of mass, force, and acceleration in a two-body system consisting of an electron and a proton. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that the center of mass of an electron and proton, when released, moves faster towards the proton. 2. **Understanding the Reason**: The reason provided states that the proton is heavier than the electron. This is true, as the mass of a proton is approximately 1836 times that of an electron. 3. **Analyzing the Motion**: When the electron and proton are released, they will exert gravitational (or electrostatic) forces on each other. According to Newton's third law, the forces are equal in magnitude and opposite in direction. 4. **Acceleration of Each Particle**: Since the proton is much heavier than the electron, it will have a smaller acceleration compared to the electron when they are attracted to each other. The acceleration \( a \) of an object is given by \( a = \frac{F}{m} \), where \( F \) is the force and \( m \) is the mass. Therefore, the electron, being lighter, will accelerate more towards the proton than the proton will towards the electron. 5. **Center of Mass Calculation**: The center of mass (CM) of a two-body system can be calculated using the formula: \[ x_{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \] where \( m_1 \) and \( m_2 \) are the masses of the electron and proton, and \( x_1 \) and \( x_2 \) are their respective positions. 6. **Behavior of the Center of Mass**: The center of mass will not move towards the proton faster; rather, it will remain stationary or move very slightly depending on the initial positions and velocities of the two particles. This is because the center of mass of the system is influenced more by the heavier mass (the proton) than the lighter mass (the electron). 7. **Conclusion**: Therefore, the assertion that the center of mass moves faster towards the proton is false. The reason that the proton is heavier than the electron is true. Thus, we conclude that the assertion is false, but the reason is true. ### Final Answer: - Assertion: False - Reason: True

To analyze the given statements, we need to understand the concepts of center of mass, force, and acceleration in a two-body system consisting of an electron and a proton. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that the center of mass of an electron and proton, when released, moves faster towards the proton. 2. **Understanding the Reason**: ...
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