Question

A body is moving in a circle at a uniform speed v. What is the magnitude of the Change in velocity when the radius vector describes an angle $\theta$

• A. $u\cos \theta$
• B. $2\nu \cos \left(\frac{\theta }{2}\right)$
• C. $\nu \sin \theta$
• D. $2u\sin \left(\frac{\theta }{2}\right)$

Answer 1

The correct option is D $2u\sin \left(\frac{\theta }{2}\right)$

$\begin{array}{c}\text{Change in velocity is given by}\\ \begin{array}{cc}\Delta V& =|{\overline{v}}_2-{\overline{v}}_1|\\ & =\sqrt{v^2+v^2+2xv\times v\cos (\pi -\theta )}\\ & =\sqrt{2v^2(1-\cos \theta )}\\ & =\sqrt{4v^2{\sin }^2\theta /2}\\ & =2v\sin \theta /2\end{array}\\ \text{Hence option}D\text{is correct}\end{array}$