14-01-09. Time to empty a sphere.

A simple one for today...

What is the time in which a sphere of radius R is emptied by a hole at the bottom of it which is of radius "a" << R

Only force is due to gravity.

**Filled with water

11 Answers

1
skygirl ·

wat is there inside the sphere??

air ??

1
skygirl ·

is it 2√(R/g) by chance ?? (little bit tukka :P)

1357
Manish Shankar ·

where is a!!!??

1
skygirl ·

it is small naa........

so....

kho gaya :P

1
skygirl ·

wont the vel of lq through the hole be same as efflux vel ... ??

1
skygirl ·

yeah one prob .... area of cross section not fixed newhere.....

huh!

me talking nonsense...

neend me socte hain iske bare me [3]

1357
Manish Shankar ·

:)

1
Aditya ·

where exactly is the hole from bottom?.....if it is at the bottommost point , time reqd shud b infinite as philip said.

1
Philip Calvert ·

hole is "at the bottom" aditya

9
Celestine preetham ·

use v=√2gh

dVolume/dt = av
express volume as function of height
and integrate to find time

1
skygirl ·

is the time...

t= 2R2/g√2Rg/(R4-a4) (1- a2/R2)

??

(most ganda ans of this new year..)

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