question_answer

A boy moving along a circular path of radius 10 m completes 3/4th of the circle in 10 s. The magnitude of speed and velocity are

A) 4.71 m/s and 47.1 m/s

B) 4.71 m/s and 1.41 m/s

C) 1.41 m/s and 4.71 m/s

D) 1.41 m/s and 1.41 m/s

Correct Answer: B

Solution :

[b] Distance \[=\frac{3}{4}\times 2\pi r\]

\[h=\frac{3}{4}\times 2\times \frac{22}{7}\times 10=47.10\operatorname{m}\]

Displacement =\[\sqrt{2r}=10\sqrt{2}\]

\[\therefore \operatorname{Speed}=\frac{Distance}{Time}=\frac{47.10}{10}=4.71\ m{{s}^{-1}}\]

\[\therefore \operatorname{Velocity}=\frac{Displacement}{Time}=\frac{10\sqrt{2}}{10}=1.41\ {{\operatorname{ms}}^{-1}}\]