Question

A point transversed $3/4^{th}$ of the circle of radius $R$ in time $T$ .The magnitude of the average velocity of the particle in this time interval is

• A. $\frac{2\pi R}{T}$
• B. $\frac{3\pi R}{2T}$
• C. $\frac{\sqrt{2}R}{T}$
• D. $\frac{\sqrt{2R}}{T}$

Answer 1

The correct option is C $\frac{\sqrt{2}R}{T}$

Initial and final positions of the point are shown in figure.

Then, displacement of point $S=\sqrt{R^2+R^2}=\sqrt{2}R$

and given time taken $=T$

Average velocity $=\frac{\text{Total displacement}}{\text{Total time}}=\frac{\sqrt{2}R}{T}$