Question

what is the numerical ratio of average velocity to average speed of minute hand of a clock when it completes half an hour​

Answer 1

answer : 2 : π

explanation : Let length of minute hand is L m.

when minute hand completes half an hour.

angular displacement, $\theta$ = 180°

so, linear displacement , s = L × 360°/180° = 2L

so, average velocity = 2L m/(30 minute)

= (2L)/(30 × 60) m/s

= L/900 m/s

distance covered by minute hand , D = 1/2 × circumference

= 1/2 × 2πL

= πL

so, average speed = πL/(30 × 60)

= πL/1800 m/s

now ratio of average velocity to average speed = (L/900)/(πL/1800)

= 2/π