Question

A motor car is moving in a circular path with uniform speed, $V$. Suddenly the car rotates through an angle $\theta$. Then, the magnitude of change in its velocity is

• A. $2V\cos \frac{\theta }{2}$
• B. $2V\sin \frac{\theta }{2}$
• C. $2V\tan \frac{\theta }{2}$
• D. $2V\sec \frac{\theta }{2}$

Answer 1

Answer: (B)

$2V\sin \frac{\theta }{2}$

The Magnitude of change in velocity $=\sqrt{v^2+u^2-2uv\cos \theta }$

$=\sqrt{v^2+v^2-2v^2\cos \theta }$ $(\because v=u)$

$=v\sqrt{2}\times \sqrt{1-\cos \theta }$

$=v\sqrt{2}\times \sqrt{2{\sin }^2\left(\frac{\theta }{2}\right)}$ $=2v\sin \left(\frac{\theta }{2}\right)$

$=2V\sin \left(\frac{\theta }{2}\right)$ $(\because v=V)$