Question

A particle is moving in a circle of radius $r$ having centre at $O$, with a constant speed $v$. The magnitude of change in velocity in moving from $A$ to $B$ is

• A. $2v$
• B. $0$
• C. $\sqrt{3}v$
• D. $v$

Answer 1

The correct option is D $v$

Magnitude of change in velocity from A to B.

Given $|{\overrightarrow{V}}_A|=V|{\overrightarrow{V}}_B|=V$

$|{\overrightarrow{V}}_A-{\overrightarrow{V}}_B|=\sqrt{V_A^2+V_B^2-2V_A{V}_B\cos \theta }$

$=\sqrt{V^2+V^2-2V^2\cos 60}$

$=\sqrt{V^2+V^2-\frac{2V^2}{2}}$

$=\sqrt{V}$

$|{\overrightarrow{V}}_A-{\overrightarrow{V}}_B|=V$