IIT JEE , AIEEE Forum - Physics , Mechanics

learner

Two nice questions, both from surface tension..

1)Find the net downward thrust on the curved surface of a bucket of height h,radii a & b,full of liquid with density d.(a<b)

2)A long wire of mass per unit length w is floating in a liquid such that the top surface of liquid dips by a distance y.If length of vessel is 2a,find surface tension of liquid.(IIT 2004)

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Rates assured..

Both are simple if you start correctly..

rohith291991

1)

h(ab+b²-2a²)dg/3

ok...i did this way.. begin by drawing the FBD of the mass m which is surrounding the inner cylinder... considering a thin slice of the bucket as i drew in the diagram...let the mass of each triangular slice be dm... then on each slice a force N will act...and the vertical component of this will balance mg and the horizontal component will balance the force F due to the cylinder...hence the net downward force due to this dm is its own weight...and by radial symmetry the net force on the curved surface is the weight of this light blue portion...the volume can easily be found using geometry and then multiply by dg to get the weight...

PS: do rate me for the diagram if u wish...it took some work..anyways i was bored...

rohith291991

2) root(a²+h²)wg/2h

the upward component of surface tension balances the weight.... see diagram..

learner

correct answer for 1)..

What I did was consider a cylindrical element of thickness dx at a depth of h....found downward force on it and then integrated it from 0 to h..

amazing diagram!!

For 2,the FBD is perfect,but there is no 'h' in the question!!

you need to make some assumptions here...including y<<a..

And the answer will be wga/2y..

rohith291991

yeah u cud use integration for d first one..but i tried to do without it...for d second one..well ur answer depends on the options...if the question setter expects an approximation.. then u must approximate..since no info is given whether the value of y is high or low...i didnt approximate...my answer is general... and sorry about the h...i usually take all heights and depths as h..and thanks about the diagram..!!

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