Relative Motion in One Dimension: Practice Problem & Solution

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): If the separation \(\vec{r}_{rel}\) is constant, it implies \(\vec{r}_{rel} \cdot \vec{v}_{rel} = 0\), meaning                         \(\vec{v}_{rel}\) is perpendicular to \(\vec{r}_{rel}\), but not necessarily zero (e.g., two particles orbiting each other at constant distance). So (A) is False.

Reason (R): Relative velocity is defined as the time derivative of the relative position vector. 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.