Relative Velocity – Magnitude – Rankers Physics

Relative Motion in One Dimension: Practice Problem & Solution

Assertion (A): The magnitude of velocity of A with respect to B will be always less than (V_A). Reason (R): The velocity of A with respect to B is given by \(\vec{V}_{AB} = \vec{V}_A - \vec{V}_B\).  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Relative Motion in One Dimension. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A): The relative velocity is \(\vec{V}_{AB} = \vec{V}_A - \vec{V}_B\). If \(\vec{V}_B)\) is in the opposite direction to \(vec{V}_A\), then \(|vec{V}_{AB}| = |vec{V}_A| + |vec{V}_B|\), which is greater than (\|vec{V}_A|\). Thus, (A) is False.

Reason (R): The definition of relative velocity of A with respect to B is \(\vec{V}_{AB} = \vec{V}_A - \vec{V}_B\). So (R) is True.

Since (A) is false and (R) is true, none of the given options are strictly correct. However, if (A) is false, options (1), (2), (3) are ruled out, leaving (4) by elimination, despite (R) being true.

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