1thnk u... i remember seein this explanation sumwer. Otherwise ma 1st ans was no change.
OKIE HERES A GUD 1 .........................
A PENDULUM HAS A MASSLESS THEAD (long) ATTACHED TO A HOLLOW METAL SPHERE FILLED WITH WATER.........
A SMALL HOLE IS MADE I THE BOTTOM MOST PART OF THE HOLLOW SHPERE WHILE THE PENDULUM WAS OSSILATING ...........
assume water flows vertically downward......
DESCRIBE THE VARIATION IN TIME PERIOD........[3]
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UP 0 DOWN 0 0 17
17 Answers
13hey...can v not simply say dat in the expression for time period, 'L' is the length fr pt of suspension to CoM of bob...here as water starts flowing out, CoM initially starts to shifr downwards...so 'L' increases and thus T increases..whn complete water flows out, CoM of hollow sphere is again its geometric centre only, thus T again becomes its original value...
thus T increases, rises to max, thn decreases agn..
3NOTE THE LAST LINE IS ALMOST EXACTLY .. NOT EXACTLY....
AND THE PART AFTER """LOOKIN CAREFULLY...""" IS BASED ON THE AREA OF CROSSECTION OF THE SPHERE WHCIH INCREASES TILL CENTRAL PART AND THEN DECREASES.....
3let height of water inside sphere be x........
let area of crossection of base be s .......
let mom. inertia of sphere abt point of suspension be ML2 NOTE SINCE L IS VERY LARGE THE OTHER TERM BECOMES NEARLY ZERO IN MOMENT OF INERTIA
[kMR2] .....
velocity of water flowin outta hole =√2gx ..
(dm/dt)v = 2gxÏs .........
now component along perp to string= 2gxs sinθ .............
Ï„ = sinθ[mgL - 2gxsÏL]
IW2 = mgL -2gxsÏL [assumption θ = sinθ] ...
w2 = (m+ÏV)gL/[ML2 + ÏVL2] - 2gÏxL/[ML+ÏVL2] ..........
NOW LUKIN CAREFULLY ....
FOR THE FIRST FEW SECONDS A CHANGE IN x WILL BRING ABT A SMALL CHANGE IN V ..
SO CLEARLY IN TERM 2 OF THE EXPRESSION WILL INCREASE SLIGHTLY ........
BUT AFTER SUMTIME THE SITUATION WILL REVERSE .........
SO TERM 2 WILL INCREASE .....................
FINALLY TERM 2 WILL BECOME 0 ..............
BECOMIN EXACTLY AS WAT IT WAS BEFORE........
3no.. its just a qualitative analysis.........
ill show u mah method ...... in dat i assumed the dm/dt force acts upward...
1mayb der it was considered since it was filled wit Hg not water. Hg density > water na? nd nyway, is the radius of bob given or not?
3ill check for the source guys ............ im sure of long thread ... sorry for not mentioning ... if i rememer they also asked us to take the water to be comin out vertically.....im a little drunk ... didnt mention these 2...
faint mem. ... fromm FIITJEE material... ill check for source and let u know
3i didnt take dat into consideration as it was given """long thread""" if i remember
9if u take it as verticaly up always wat ur saying is right
but then i think its radially acting as hole being small water is spurted out in radial direction
1mayb due 2 change in centre of mass? i mean d distance of it so it increases or sumthin the length....nd den d change...i too rememebr seein d question sumwer
3i got it as the time period increases to a maximum value and then decreases to original value............ i dunno answer... saw problem sum where........
1y d variations? mass change wont affect surely? or sumthin else changin...