Question

A particle moves in a circular path with uniform speed v. When it turns by 90°, find ratio of \(\frac{v}{<\overrightarrow{v}>}\)?

• A. \(\frac{\pi}{\sqrt{2}}\)
• B. \(\frac{2\pi}{\sqrt{2}}\)
• C. \(\frac{\pi}{2}\)
• D. \(2\pi\)

Answer 1

The Correct Option is A

\(|<\overrightarrow{v}>|=\frac{|displacement|}{time}=\frac{\sqrt{2}R}{\frac{\pi R}{v}}=\frac{\sqrt{2}v}{\pi}\)
\(\frac{v}{<\overrightarrow{v}>}=\frac{v}{(\frac{\sqrt{2}v}{\pi})}=\frac{\pi}{\sqrt{2}}\)

So, the correct answer is (A): \(\frac{\pi}{\sqrt{2}}\)