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INPHO

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We don't have even 15 days for preparing .Hence i think we should prefer just discussing only few important topics via questions.

----Note

---1. Pls ensure that ques deals more with physics and less with maths(though i love such questions)

---2. Before posting Ensure that ques is really of INPHO level.

---3.Ques which involve dealing with major Topics are Welcomed.

---4.The one who solves any particular q needs to post the next q within 3 hrs.

Note by Aryan Goyat
1 week, 1 day ago

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here is another question!!

Natural uranium consists of mainly two isotopes, \(U^{238}\) and \(U^{235}\),whereas the relative concentration of the latter is 0.7%.Uranium is "enriched"(ie., concentration of \(U^{235}\) is increased) by implementing a multi-stage process,where at each stage,evaporated chemical compound \(UF_{6}\) is led through a porous wall.the porous wall can be considered to be a thin film having microscopic holes in it.How many stages are nedded to double the concentration Rohith M.Athreya · 1 week ago

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@Rohith M.Athreya iska to bta do Aryan Goyat · 6 days, 21 hours ago

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@Aryan Goyat

Take a look at the thin rod(of length \(a\)) above.

The mass density along the rod varies as \(\sigma=\sigma_{0}(1+\frac{x^{n}}{a^{n}})\) where \(n\) is a positive integer.

While calculating the co-ordinates of the centre of mass of the rod, we assume(wrongly) the COM to be at the geometric centre ie., \((\frac{a}{2},0)\)

Now, we know that's wrong and find the actual co-ordinate.

We note that the actual \(x\) co-ordinate is \(\frac{a}{2}+\delta X\) where \(X\) is the actual co-ordinate of the COM.

Define \(100\frac{\delta X}{X}\) as percentage error

Approximately what maximum percentage error will we have made in assigning the COM to rods from \(n=1\) to \(n=20\) ie.,\(\displaystyle \frac{100}{20} \sum_{n=1}^{n=20} \frac{\delta X_{n}}{X_{n}}\) where \(X_{n}\) is the COM when \(n\) is the exponent of \(x\) in the surface density expression

Details and Assumptions

the \(21^{st}\) harmonic number \(H_{21}\) = 3.645

\(1/23 + 1/24 + 1/25 = 0.12514\)

give your answer to the nearest integer Rohith M.Athreya · 1 day, 21 hours ago

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@Rohith M.Athreya an APHO type problem Rohith M.Athreya · 1 day, 21 hours ago

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@Aryan Goyat u are wrong coz u probably took ratio of masses as 238/235

take ratio of masses of uf6 Rohith M.Athreya · 5 days, 21 hours ago

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@Aryan Goyat you are off by 53 stages Rohith M.Athreya · 6 days, 21 hours ago

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@Rohith M.Athreya yep now i am getting 163 .(really what a mess i did) Aryan Goyat · 5 days, 18 hours ago

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@Aryan Goyat :) I realised Ur mistake because I did the same mistake first :p Rohith M.Athreya · 5 days, 18 hours ago

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@Rohith M.Athreya 110 stages ?? Aryan Goyat · 1 week ago

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Rajdeep Dhingra · 1 week ago

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@Rajdeep Dhingra Another such seemingly simple problem simple trick Rohith M.Athreya · 2 days, 18 hours ago

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@Rohith M.Athreya Nice problem it is . Aryan Goyat · 2 days, 17 hours ago

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@Rajdeep Dhingra but it isn't INPHO level, is it ? Shubham Dhull · 1 week ago

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@Shubham Dhull No it is as it is not that much tricky Though by the name it may suggest it uses a trick but actually it is a widely used technique which may be asked in inpho. Aryan Goyat · 1 day, 18 hours ago

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@Rajdeep Dhingra Isn't it \(\frac{2xg}{H}\) ? Sumanth R Hegde · 1 week ago

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@Sumanth R Hegde No. Rajdeep Dhingra · 1 week ago

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@Sumanth R Hegde is it 4xg/H ? Aryan Goyat · 1 week ago

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@Aryan Goyat yes! it must be 4xg/h because when u push it in, liquid moves up so that volume of wood submerged is more Rohith M.Athreya · 1 week ago

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@Aryan Goyat Correct Rajdeep Dhingra · 1 week ago

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@Sumanth R Hegde I am also getting 2xg/H. Archit Agrawal · 1 week ago

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@Archit Agrawal Wrong Rajdeep Dhingra · 1 week ago

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BTW,u could try my question simplified complications for practice

the numbers sure are weird but share the expressions u get for the radius Rohith M.Athreya · 5 days, 3 hours ago

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@Rohith M.Athreya i dunno unimodulr constnt would you tell bout it ? Shubham Dhull · 5 days ago

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@Shubham Dhull a unimodular constant means a quantity with magnitude1

for example, 1m is a unimodular constant Rohith M.Athreya · 5 days ago

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@Rohith M.Athreya lol , i did't knew it :P Shubham Dhull · 4 days, 23 hours ago

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the line shown in fig. is string not spring ( understood what i mean ?) k is given , mass is given , find whether they do s.h.m or not, if yes find the time period . if not , state under what condition can they do so . they refer to he circles made which in the figure represent cylinders assume pure rolling ( you may argue about the decreasing normal reaction, assume infinite c. of friction . the angles in figure are 30,30,120 which you can assign by just looking at the figure :) this is original . Shubham Dhull · 1 week ago

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@Shubham Dhull isn't anybody participating ? Shubham Dhull · 5 days, 23 hours ago

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@Shubham Dhull nobody dares to do my problem ? :P Shubham Dhull · 1 day, 20 hours ago

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@Shubham Dhull i didnt quite understand the setup fully

that connecting moves through the wedge?? Rohith M.Athreya · 1 day, 20 hours ago

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@Shubham Dhull if u could add what kind of displacement are u giving

are you shifting it kepping string inclined at same angle as that of equillibrium position

or are you displacing only one mass kepping the other non disturbed

or ? Aryan Goyat · 5 days, 17 hours ago

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@Aryan Goyat no, displacing both about euil. , you can do that too when only the 10 kg one is moved . Shubham Dhull · 5 days, 17 hours ago

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@Shubham Dhull no abt equilibrium but how abt equilibrium

both down

or one up other down Aryan Goyat · 5 days, 17 hours ago

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@Aryan Goyat i didn't get what u r saying . Shubham Dhull · 5 days, 17 hours ago

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@Shubham Dhull try with spring too ..:) Shubham Dhull · 1 week ago

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@Shubham Dhull the bottom one depicts equilibrium position Aryan Goyat · 5 days, 17 hours ago

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@Aryan Goyat erh...then......what about it ? what you have drawn is common sense :P , no need to draw , i didn't just understand ur language , i want you to prove it does / or not s.h.m by condition of shm i.e f =kx and find time period . hint : since it is string, it'll apply force only when extended . ;) Shubham Dhull · 5 days, 17 hours ago

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@Shubham Dhull they r both dragged down by same force || to the /\ planes ;) Shubham Dhull · 5 days, 17 hours ago

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@Shubham Dhull yahi to puch raha tha dhanyvad :p Aryan Goyat · 5 days, 17 hours ago

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@Shubham Dhull

Aryan Goyat · 5 days, 17 hours ago

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@Shubham Dhull the wedge is fixed . Shubham Dhull · 1 week ago

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isn't anybody participating ? Shubham Dhull · 1 week, 1 day ago

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Let L1 be the present total angular momentum of the Earth-Moon system. Now, make the following assumptions: i) L1 is the sum of the rotation of the Earth around its axis and the translation of the Moon in its orbit around the Earth only. ii) The Moon’s orbit is circular and the Moon can be taken as a point. iii) The Earth’s axis of rotation and the Moon’s axis of revolution are parallel. iv) To simplify the calculations, we take the motion to be around the center of the Earth and not the center of mass. Throughout the problem, all moments of inertia, torques and angular momenta are defined around the axis of the Earth. v) Ignore the influence of the Sun. 1a Write down the equation for the present total angular momentum of the Earth-Moon system. Set this equation in terms of E I , the moment of inertia of the Earth; ωE1 , the present angular frequency of the Earth’s rotation; M1 I , the present moment of inertia of the Moon with respect to the Earth´s axis; and ω M1 , the present angular frequency of the Moon’s orbit Shubham Dhull · 1 week, 1 day ago

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@Shubham Dhull Isn't it L1 = (E I)(wE1) + (M1 I)(w M1) ? Rajdeep Dhingra · 1 week, 1 day ago

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@Rajdeep Dhingra i think that must be so .pls post the next q. Aryan Goyat · 1 week ago

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@Rajdeep Dhingra Ya that's quite apparent.you can access the full prob.it gets more interesting after.ipho 2009/10(most prob) Spandan Senapati · 1 week, 1 day ago

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OK guys here is my first question

1--- A small ball moves at a constant velocity v along a horizontal surface and at a point A falls into a vertical cylindrical well of depth H and radius r.The velocity v of the ball forms an angle alpha with the diameter of the well drawn through point A. Determine relation b/w v,r,H and alpha so that ball gets out of well after elastic impact.(take all collision to be elastic +friction=0)

(u don't need to solve any ques to post your ques if you have one please post it and share this note with as much people as you can) Aryan Goyat · 1 week, 1 day ago

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@Aryan Goyat OK I have solved this.we can take the projection of the motion on a horizontal plane.the problem then reduces that the velocities get reflected along a normal to a point at which the ball stikes in the plane.so we can conclude mathematically that in a circle I take a line with @ angle to the horizontal and every time it strikes the circle it gets reflected.then the length of that segment is 2rcos@ and of I keep on doing so at some time I must return to the original point.the total length is then 2nrcos@.and this must be vk2√2h/g.as v in the projected plane is constant.and the constant 2with √2h/g for the cyclic process Spandan Senapati · 1 week, 1 day ago

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@Aryan Goyat nrcos(alpha)=kv√(2H/g) where n and k belong to integers. Archit Agrawal · 1 week, 1 day ago

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@Archit Agrawal yes , that's what i get if alpha is 0, so i guess u r right :) Shubham Dhull · 1 week, 1 day ago

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@Aryan Goyat can you attach a a pic ?because you say the velocity of ball is parallel to hori. and the well is vertical so in this case alpha is 0 , right ? by the way in this case i get answer as r=v*root(2h/g) is it right ?if alpha=0 ? Shubham Dhull · 1 week, 1 day ago

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@Shubham Dhull It means that the balls velocity was initially in a horizontal plane with an angle alpha to the actual horizontal line. Spandan Senapati · 1 week, 1 day ago

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@Aryan Goyat Krotov question I guess?? Spandan Senapati · 1 week, 1 day ago

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@Spandan Senapati Yes Archit Agrawal · 1 week, 1 day ago

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