A particle is moving with constant speed under root 2 metre per second with on a circular path of radius 10 cm find the magnitude of average velocity when it has covered three-fourth circular path.
Answers
Answer:
Given:
Object is moving with a speed of √2 m/s.
Radius of circle = 10 cm = 0.1m
To find:
Average velocity when the object has covered ¾ circular path
Concept:
Average velocity is the ratio of displacement to the time taken.
Avg. Velocity = (displacement)/(time)
Now , since we are dealing with displacement, we need to find the shortest distance between starting and stopping point.
Diagram:
Please refer to the attached photo to understand better.
Calculation:
Time taken = (distance)/(velocity)
=> time = {¾ (2πr) }/ √2
=> time = {¾ ( 2 × π × 0.1)} / √2
=> time = [(3/√2) × (0.1) × π]
Now displacement can be found using Pythagoras theorem.
CD is the shortest distance and hence is the displacement.
CD² = OC² + OD²
=> CD² = (0.1)² + (0.1)²
=> CD = [(0.1) × √2]
So average velocity
= (CD)/time
=[(0.1) × √2]/ [(3/√2) × (0.1) × π]
= 6π m/s.
Answer:
For showing Full answer click on photo.
