Question

A particle is moving in a circular path of radius 1 m with uniform speed $5\sqrt{5}{ms}^{-1}$ as shown in figure.
The magnitude of change in velocity between points A and B is

• A. Zero
• B. $20{ms}^{-1}$
• C. $10\sqrt{2}{ms}^{-1}$
• D. $3\sqrt{5}{ms}^{-1}$

Answer 1

The correct option is C $10\sqrt{2}{ms}^{-1}$

$\begin{array}{c}\text{Given is a uniform circular motion, with}\\ \text{constant speed}=5\sqrt{5}m/s\\ \text{velocity at}A\left({\overrightarrow{v}}_A\right)=\left(5\sqrt{5}\hat{j}\right)m/s\end{array}$

$\text{velocity at}B\left({\overrightarrow{v}}_B\right)=-5\sqrt{5}(\cos {37}^{\circ }j+\sin {37}^{\circ }\hat{1})m/s$

$=-\sqrt{5}(3\hat{i}+4\hat{j})m/s$

$\text{Thus, change in velocity}\begin{array}{cc}={\overrightarrow{v}}_B\overrightarrow{v_A}& =\left[\sqrt{5}\right(3\hat{i}+4\hat{j})-5\sqrt{5}\hat{j}]m/s\\ & =-\sqrt{5}(3\hat{i}-9\hat{j})m/s\end{array}$

$\begin{array}{cc}\text{Hence, required magnitude}& =\sqrt{5}\cdot \sqrt{3^2+9^2}m/s\text{.}\\ & =15\sqrt{2}m/s\end{array}$