The figure shows a body of mass $m$ moving with a uniform speed $v$ along a circle of radius $r$. The change i

Question

The figure shows a body of mass $m$ moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is:

Accepted Answer

1.  **Vector Difference:** The change in velocity $\Delta \mathbf{v}$ is the vector difference between the final velocity $\mathbf{v}_B$ and the initial velocity $\mathbf{v}_A$: $\Delta \mathbf{v} = \mathbf{v}_B - \mathbf{v}_A$ .
2.  **Uniform Circular Motion:** In uniform circular motion, the speed remains constant ($|\mathbf{v}_A| = |\mathbf{v}_B| = v$), but the direction changes .
3.  **Calculation:** Assuming points A and B subtend an angle of $90^\circ$ at the center (implied by the standard result $v\sqrt{2}$ for a quarter circle path), the angle between the velocity vectors $\mathbf{v}_A$ and $\mathbf{v}_B$ is also $90^\circ$.
    Using the law of vector subtraction:
    $|\Delta \mathbf{v}| = \sqrt{v^2 + v^2 - 2v^2 \cos(90^\circ)}$
    $|\Delta \mathbf{v}| = \sqrt{v^2 + v^2 - 0} = \sqrt{2v^2} = v\sqrt{2}$.

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