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Please help!

Please help me in the 7th question....

Note by A E
8 months, 1 week ago

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Any suggestion on coordinate geometry, I am very weak in it?

Harsh Shrivastava - 8 months, 1 week ago

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Hey you like integrals.I have a good one1)\(int1/(a+b(1-x))^2dx\)with x varying from \(0-1\).This is a Feynman's Puzzle.Looks easy but needs some more....

Spandan Senapati - 8 months ago

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use the transformation x-> 1-x and then differentiate the function 1/(a+bx) wrt a and then done.

Harsh Shrivastava - 8 months ago

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@Harsh Shrivastava And also try to read "Feynman's trick"of differentiation under the integral sign.You will surely like it.

Spandan Senapati - 8 months ago

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@Spandan Senapati I just know how to apply it I don't know the technalities behind it, will study soon.

Harsh Shrivastava - 8 months ago

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@Harsh Shrivastava OK ok.That will lead to answer of \(I=1/ab\).If a and b are of opposite sign then the integrals value is Negative \((ab<0)\).But the integrand be a square the area can never be negative.How do you resolve this...Here you integrating through Singularities.Pretty much the same thing as \(dx/x^2\) integral from (-1 to 1) isn't -2.The function blows up when x-->0...That's why its a Feynman's Puzzle...Try using limits in integrand.

Spandan Senapati - 8 months ago

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Which part...I guess straight lines and circles you must be well acquainted with......Coordinate needs some heavy practice....Formulas and all those stuffs should be known all the time..?As such I don't follow any special book only fiitjee package.

Spandan Senapati - 8 months ago

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TMH and archive will suffice.

A E - 8 months, 1 week ago

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Hey in your q you talked abt Max area....I think it should be min.I did it as the req point of intersection is \(apq,a(p+q)\) where the points P and Q are \((ap^2,2ap)\)and \((aq^2,2aq)\).Then the cond yields \(apq=-1\).Vertex being \((0,0)\)The Area of \(PCQ\) is \(a^2|pq(p-q)|\).Puting \(pq=-1/a\) And later applying AM-GM yields the ans as \(Min=1\).\(a=1/4\) from \(y^2=4ax\)

Spandan Senapati - 8 months ago

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Yeah you are right, my mistake, edited!

Harsh Shrivastava - 8 months ago

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@Harsh Shrivastava Ya I see the problem has been changed.Thanks....I was surprised because of the title "its right"....I accepted my ans to be wrong....

Spandan Senapati - 8 months ago

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Use the fact that since we assume strings to be inextensible, velocity of M at bottommost point will be only in horizontal direction, and use constraint relation between the velocity of M and m by equating their velocities along the thread connecting them.Finally use energy conservation.

Harsh Shrivastava - 8 months, 1 week ago

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Thanks Harsh & Spandan.

A E - 8 months, 1 week ago

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I got it. Will post a solution by night.

Harsh Shrivastava - 8 months, 1 week ago

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@Spandan Senapati

A E - 8 months, 1 week ago

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Ya I know this q.Follow Harsh s solution.And you will get it.And if any problem then tag me and I will post it.Ok

Spandan Senapati - 8 months, 1 week ago

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Hey Spandan ,AE can you guyz tell me good source for practicing mechanics questions, especially rotational mechanics?

Harsh Shrivastava - 8 months, 1 week ago

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@Harsh Shrivastava Irodov(that's too good a book as I felt for rotational mech),and hc verma is good as well.For more tough prob you can refer to 300 creative physics problems by Laszlo Holics.

Spandan Senapati - 8 months, 1 week ago

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@Spandan Senapati yes, i have done that book it's amazing.

Brilliant Member - 8 months ago

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@Brilliant Member Then try this "A guide to physics problems"... May be the second part be a bit tough as its Mostly Quantum Electrodynamics,Quantum Mechanics and all those stuffs but part 1 is good...... You will surely like it..And also try the integral I have posted

Spandan Senapati - 8 months ago

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@Spandan Senapati dekhunga abhi ke liye toh jee bhot h :P

Brilliant Member - 8 months ago

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@Brilliant Member pdf h iskki ?

Brilliant Member - 8 months ago

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@Brilliant Member No my sir had given me...Not now but do try after you go an iit

Spandan Senapati - 8 months ago

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@Spandan Senapati yes sure , why not ? i'll be doing mechanics for next 3 days even though i have chem exam ;P

Brilliant Member - 8 months ago

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@Spandan Senapati Ya....that book is very good.

A E - 8 months ago

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@Brilliant Member Complete??good.I just solve in leisure....

Spandan Senapati - 8 months ago

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@Spandan Senapati nah, not completely though ;P

Brilliant Member - 8 months ago

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@Brilliant Member I used to solve some each day before inpho but now I have made up a plan to complete It.

Spandan Senapati - 8 months ago

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@Spandan Senapati nice , it's an awesome book , go for it.

Brilliant Member - 8 months ago

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@Spandan Senapati Yes irodovs questions are good they are good but they are repeated in many books.

Harsh Shrivastava - 8 months, 1 week ago

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@Harsh Shrivastava Further you may try David morin and peter gnadig's book " 200 puzzling questions in physics"

A E - 8 months, 1 week ago

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@A E But answer to David Morin's questions are not available? Do u have them?

Harsh Shrivastava - 8 months, 1 week ago

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@Harsh Shrivastava I feel the questions in Problems section are good enough .These problems have detailed solution which should be enough I guess.

A E - 8 months, 1 week ago

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