question_answer

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:

A)  \[v\sqrt{2}\]          

B)  \[v/\sqrt{2}\]

C)  \[v\]             

D)  zero

Correct Answer: A

Solution :

 When a body rotates uniformly, then the direction of velocity changes continuously but its magnitude remains constant. Also, direction of velocity is perpendicular to direction of motion. \[\therefore \] \[{{\vec{v}}_{A}}=\hat{j}\,\,\vec{v},\,\,{{\vec{v}}_{B}}=-\hat{i}\,\,\vec{v}\] Change in velocity \[\Delta \,\vec{v}={{\vec{v}}_{B}}-{{\vec{v}}_{A}}\] \[=-\hat{i}\,\vec{v}-\hat{j}\,\vec{v}\] Magnitude of change in velocity is \[=\left| -\hat{i}\,\vec{v}-\hat{j}\,\vec{v} \right|=\sqrt{{{v}^{2}}+{{v}^{2}}}=v\sqrt{2}\]