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Assertion : An object has given two velo...

Assertion : An object has given two velocities `vecv_(1)` and `vecv_(2)` has a resultant velocity `vecv = vecv_(1) + vecv_(2)`.
Reason : `vecv_(1) and vecv_(2)` should be velocities with reference to some common reference frame.

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The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion:** The assertion states that if an object has two velocities, \( \vec{v_1} \) and \( \vec{v_2} \), then the resultant velocity \( \vec{v} \) can be expressed as: \[ \vec{v} = \vec{v_1} + \vec{v_2} \] This is a fundamental concept in vector addition. When two vectors are added, the resultant vector can be found using the parallelogram law of vector addition. **Hint:** Recall how vector addition works geometrically. 2. **Analyzing the Reason:** The reason states that \( \vec{v_1} \) and \( \vec{v_2} \) should be velocities with reference to a common reference frame. This is crucial because vectors are dependent on the frame of reference from which they are measured. If \( \vec{v_1} \) is measured from one frame (e.g., a moving train) and \( \vec{v_2} \) from another (e.g., a stationary ground), their direct addition would not yield a valid resultant. **Hint:** Consider how different frames of reference can affect the measurement of velocities. 3. **Conclusion about Assertion and Reason:** Both the assertion and the reason are true statements: - The assertion correctly describes how to find the resultant of two velocities. - The reason correctly emphasizes the necessity of a common reference frame for the velocities to be added meaningfully. However, the reason does not directly explain the assertion. The assertion is about the mathematical operation of vector addition, while the reason discusses the conditions under which this operation is valid. **Hint:** Think about the relationship between the validity of vector addition and the conditions under which it is performed. ### Final Answer: Both the assertion and the reason are true, but the reason does not explain the assertion.
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