Question

a can filled with water is revolved in a vertical circle of radius 4m so that the water does not fall down. the maximum possible period of revolution is:

a) 1s
b) 2s
c) 3s
d) 4s

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

Critical velocity at highest point(Vc) =√rg= √4×10=√40m/sec.                                          Distance covered in one revolution (s)=2πr=2×3.14×4m.                       time taken for a revol. (t)=s÷Vc= 2×3.14×4÷√40= 4sec....(about)