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Assertion:- If at t=0, centre of mass of...

Assertion:- If at t=0, centre of mass of an isolated system is at (0,1,2) than at t=2h,25 min, its centre of mass may be (0,1,2).
Reason:- For a isolated system, velocity of the centre of mass is constant.

A

If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.

B

If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.

C

If Assertion is True but the Reason is False.

D

If both Assertion `&` Reason are False.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the assertion and the reason given in the question. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that if the center of mass (CM) of an isolated system is at (0, 1, 2) at time t = 0, then at t = 2 hours and 25 minutes, the center of mass may still be at (0, 1, 2). - This implies that the position of the center of mass does not change over time. 2. **Understanding the Reason**: - The reason states that for an isolated system, the velocity of the center of mass is constant. - In an isolated system, there are no external forces acting on it, which means the net external force is zero. 3. **Analyzing the Isolated System**: - Since the system is isolated, the acceleration of the center of mass can be calculated using Newton's second law: \[ a_{CM} = \frac{F_{external}}{M} \] where \( F_{external} = 0 \) (because the system is isolated) and \( M \) is the total mass of the system. - Therefore, the acceleration of the center of mass \( a_{CM} = 0 \). 4. **Implications of Zero Acceleration**: - If the acceleration is zero, it means the velocity of the center of mass is constant. - If the initial velocity of the center of mass is zero, it will remain at rest, and thus the position will not change over time. 5. **Conclusion**: - Since the center of mass can remain at the same position (0, 1, 2) if it started from there with zero velocity and no external forces acting on it, the assertion is true. - Additionally, the reason provided correctly explains why the assertion is true, as it states that the velocity of the center of mass remains constant in an isolated system. ### Final Answer: Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.
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