Question

A car is moving on a circular path with constant speed 10 m/s. What is the change in velocity when it moves through ${120}^{\circ }$?

• A. $5\sqrt{2}m/s$
• B. $10\sqrt{3}m/s$
• C. $\sqrt{3}/10$ $m/s$
• D. $5\sqrt{3}m/s$

Answer 1

The correct option is B $10\sqrt{3}m/s$

$\begin{array}{c}\text{Given,}R=\text{radius of circular path.}\\ \text{Also, speed of uniform circular motion}=10m/s\\ \text{Thus,}{\overrightarrow{v}}_A=\left(10\hat{i}\right)m/s\\ \text{and}{\overrightarrow{v}}_B=10(\cos {60}^{\circ }i+\sin {60}^{\circ }\hat{j})m/s\\ =5(-i+\sqrt{3}\hat{j})m/s\end{array}$

$\begin{array}{cc}\text{Therefore, change in velocity}& ={\overrightarrow{v}}_B\overrightarrow{v_A}\\ & =-15i+5\sqrt{3}\hat{j}\\ \text{Herce, magnitude}& =\sqrt{{15}^2+5{\sqrt{3}}^2}m/s.\\ & =10\sqrt{3}m/s.\end{array}$