Question

A wet open umbrella is held vertical and whirled about the handle at a uniform rate of 21 rev in 44 s. If
the rim of the umbrella is a circle of 1 m in diameter and the height of the rim above the floor is 4.9 m.
The locus of the drop on the floor is a circle of radius:​

Answer 1

Answer:

1.5 m

Explanation:

rim radius = 1/2 m

revolutions = n = 21 per 22s

v = r w ; w = angular velocity = 2πn/t

v = 1/2 × 2 × 22/7 × 21 / 44

v = 1.5 m/s

now h = 4.9 m

h = 1/2gt^2

4.9 = 1/2 (9.8) × t × t

t = 1 sec

the drop (projectile) range = v × t

hence it's radius = 1.5 × 1 = 1.5 m

Note :

the drops behave like, projectile with velocity v and fall parabolically on the ground in a circular path. they have no acceleration bcoz horizontal