Question

A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

Answer 1

At the top most position

three forces will act on the water

1 weight in the downward direction

2 normal reaction by bucket in the downward direction

3 centrifugal force in the upward direction

so mg + N =mv2/r

for water just does not fall N ≥ 0

so mg = mv2/r

v =√gr

so time period T = 2∏r/v

=2*3.14*4 /√4g

=3.14*4 /√9.8

=4.01

it is approx.

Answer 2

Answer:

ANSWER

For the water not to fall down, the weight of the water must be balanced by the centrifugal force.

mg=m  

r

v  

min

2

​  

 

​  

 

v  

min

​  

=  

gr

​  

 

For 1 revolution,

v=  

T

2πr

​  

 

∴T=  

v

2πr

​  

 

∴T=  

gr

​  

 

2πr

​  

 

∴T=2π  

g

r

​  

 

​  

 

∴T=  

g

​  

 

4π

​  

 

⟹T=4.01 sec