A ball moves one-fourth `((1^(th))/(4))` of a circle of radius R in time T. Let `v_(1)` and `v_(2)` be the magnitudes of mean speed and mean velocity vector. The ratio `(v_(1))/(v_(2))` will be

Options

A. `pi/2`
B. `3/pi`
C. `(2)/(sqrt(3)pi)`
D. `(pi)/(2sqrt(2))`

Answer

D

Explanation

Key Idea Mean of a moving body,
`v_("rms")=("total distance")/("total time taken")`
Mean velocity vector for a moving body,
`v_("vv")= ("total displacement")/("total time taken")`
A ball moving in a circular arc is shown in the figure below,
Here, `v_("rms")= (2 pi R)/(4)xx1/T= v_(1)`
Similarly, `v_("vv")=(sqrt(2)R)/(T)`
Hence, `(v_(1))/(v_(2))=(pi)/(2sqrt(2))`
Option (d) is correct.