Question

The time period of a pendulum, whose bob is hollow and filled with water, is noted down. If a hole is made in the bob of the pendulum such that the water starts leaking, then how would the time period of the pendulum be affected?
I mean it would increase, decrease or remain constant and why?

Answer 1

@ghazi , @UnkleRhaukus
plz help me with this question
i really don't have much time as i have my exams starting in 5 days. plz help.

Answer 2

time period will decrease....gradually

Answer 3

may i know why?

Answer 4

just consider an example that...if you hook a weight of 10 kg and then you hook weight of 10gm ....surely time period of 10 kg would be higher than that of 10gm not because of mass but because of air resistance and capability of heavier mass to overcome that ...(damped oscillation)

Answer 5

but air resistance depends on the shape/size and in this case none of them would change

Answer 6

hmm....okay...just let them be sphere of 10gm and 10kg now?

Answer 7

now which one has ability to overcome air resistance easily 10kg or 10gm?

Answer 8

okay even if i accept your reasoning, the answer would be a decrease in the time period but the book i got the question from says that the time period would first increase and then decrease (no reason )

Answer 9

may be question says that initially bob was hollow and readings were taken..then water filled in it after that there was an increase in time period....followed by a hole in it ....which again leads to the lowered time period.....

Answer 10

well,the question is this only as far as i remember (i don;t have the book handy right now) but don;t you think that the question can be based on the dynamics of the falling water! (i have no idea about it - just a thought)

Answer 11

well dynamics will make it too complex...and that will be take in count if the flow of water through bob has to be considered ....so i guess No

Answer 12

well, ok thanks for your time, ireally got to go know.

Answer 13

* i really
* know- now

Answer 14

:)

Answer 15

i guess it will remain constant as it ideally depends on length of podulum not on the weight of it.....as
\[t=2\pi \sqrt{\frac{ l }{ g }}\]

Answer 16

the time period will increase first and then it will suddenly fall back to the initial value...
according to the above mentioned formula we see that time period is directly proportional to sqrt(effective length)....as the water start to come out of the ball...the centre of gravity of the system( bob+water) will shift lower that will cause an increase in the effective length increasing the time period

Answer 17

but as soon as total water comes out of the bob, the centre of gravity will shift back to the original position....and so the time period falls sharply back to the initial value

Answer 18

@akash123 thnx for the answer
i geddit

Answer 19

:)