Question

find ratio of average speed and magnitude of average velocity of tip of minute hand in 20 minutes ​

Answer 1

Let the length of minute hand is r m.

given, tip of minute hand in 20 minutes.

so, distance covered by minute hand = (2πr/60) × 20 = 2πr/3 m

so, average speed = distance covered/time taken

= (2πr/3)/(20 × 60) m/s

= 2πr/3600 m/s ......(1)

displacement of minute hand during 20 minute = 2rsin60° = √3r m

so, average velocity = √3r/(20 × 60) m/s....(2)

from equations (1) and (2),

average speed /average velocity = 2π/√3

hence, ratio is 2π : √3

Answer 2

Answer:

2π/3√3

Explanation:

length of the minute hand = l m

distance travelled in 20 minutes :

speed of minute hand *20

(2πl/60)*20 = 2πl/3 m

average speed :

distance/time = (2πl/3)/(20*60)

=> πl/1800 m/s

displacement in 20 minutes:

=> 2l Sin60°

=>2l * √3/2

=> √3 l

average velocity :

displacement / time = √3 l / (20*60)

=> √3 l/ 1200

average speed :average velocity

=> πl/1800 : √3l / 1200

=> 2π/3√3 Ans.