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A solid metallic sphere in a uniform electric field..how to draw..lines of force Now if the solid metallic sphere is to be replaced by a hollow metallic sphere, how will the field lines look like. Again draw the lines of forc ...

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A simple one What is the minimum velocity you have to hit a charge q at a distance D from the center of a ring radius R and charge Q towards it along the central axis so that it stops at the center of it? Clarification: The r ...

At the center or a neutral hollow metallic shell, a point charge is placed Is it a point of equilibrium? if yes what kind of equilibrium? ...

A turntable rotates with constant angular speed \Omega . A ball rolls on it,without slipping .the ball has uniform mass density , so moment of inertia is I=\frac{2}{5}MR^2 show that whatever the (non -slipping )initial condit ...

Which of these is greatest .9 (0.9999999999999999999................) 1.01 (1.00000000000000.................0001) 1 ?? ...

Q1) Using Vander waal's equation of state, find the pressure at which the PV vs P curve acquires minima for 1.0 mole of oxygen gas at 0°C . a = 1.36 L2 atm mol-2 and b = 32 cm3mol-1 Q2) A beam of X-rays is scattered by loose ...

PS : It's 22nd now so I'm allowed to post the question :P *Image* ...

Prove Perpendicular and Parallel axis theorem. Hint: for perp axis thm: Think of why Ix+Iy=Iz is valid only on one plane :P I was teaching recently and suddenly wondered why i never asked this as a QOD here :P ...

The first two questions were the very first tough questions I did(from Alkyl Halides too)...way back in the beginning of class 12th FIITJEE. Let's see how you all fare! *Image* Lo yaar hint lo....think Favorskii reaction. ...

Today's question has three parts(fairly easy) -: (a) The rate law for the substitution reaction of 2-bromobutane and HO- in 75% ethanol/25% water at 30°C is given as Rate = 3.2 x 10-5 [2-bromobutane][HO-] + 1.5 x 10-6[2-brom ...

A Conducting Sphere S1 of radius 'r' is attached to an insulating handle. Another conducting sphere S2 of radius 'R' is mounted on an insulating stand. S2 initially uncharged. S1 is given a charge Q, brought into contact with ...

Thought of posting a little quickie here since I have the rights... Predict the products and explain the mechanism for the following reaction(s) -: *Image* Note : Oldies to whom I have explained this reaction are not allowed ...

A cylinder of mass M is placed on the top of a block of mass 2M. Neglect the friction between block and the horizontal plane . But friction coefficient between cylinder and the top surface of the block is \mu . A small body o ...

A cylinder of mass M and radius R is rotated in a uniform V groove with constant angular velocity ω. The coefficient of friction between cylinder and each surfave is μ. What torque must be applied to the cylinder to keep it ...

Let C1 and C2 be the graphs of the function y = x2 and y = 2x, 0<x<1 respectively. Let C3 be the graph of a function y = f (x), 0<x<1, f(0) = 0. For a point P on C1, let the lines through P, parallel to the axes, ...

If a and b are 2 integers such that 7 divides a2+b2, show that 49 divides a2+b2 (Slight olympiad tilt here) ...

Show that a(a-b)(a-c)+b(b-c)(b-a)+c(c-a)(c-b) cannot be negative This i saw in a website online.. i liked this one because it does not even require AM GM ;) ...

What is the path of an electron if the magnetic filed is shown as in the image. The field is outward and has values B and 2B on either sides of the line. The region is infinite on both sides.... Trace the shape of the path of ...

More Integration.... 1) \int{\frac{{dx}}{{\sqrt{\cos^{3}(x+\alpha )\sin (x+\beta )}}}} 2) \int{\left({x^{7m}+x^{2m}+x^{m}}\right)}\left({2x^{6m}+7x^{m}+14}\right)^{1/m}dx 3) \int{\frac{{dx}}{{\sqrt x+\sqrt{1-x}}}} (Same comme ...

*Image* The image above is a koch Snowflake starting with a equilateral triangle of side 1 unit Step One. Start with a large equilateral triangle. Step Two. Make a Star. 1. Divide one side of the triangle into three equal par ...

This one is a question someone asked me a few days back.. I guess it is from a ISI paper... (I may be wrong!) There is a matrix which is NxN Each element is filled with either 1 or -1 with an equal probability. What is the pr ...

What is the value of cot-1(-2)+cot-1(-3) ? (A simple one which ppl often make mistakes at) ...

We all know that the path of a projectile is a parabola. My claim is that if we threw a stone in real life (Even without air friction), it will not follow a parabolic path. Am I correct? If yes, then what will be the path. If ...

Evaluate the following integral: \int_{-100}^{-10}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2\mathrm dx+\int_{\frac{1}{101}}^{\frac{1}{11}}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2\mathrm dx + \int_{\frac{101}{100}}^{\frac{11}{10}}\l ...

1) Aspirin is a pain killer with pKa=2. 2 tablets each containing 0.09 gm of aspirin are dissolved in 100ml solution. Resultant pH = ----------- 2)if rain water consists of 2.463 lt of dissolved SO3 in 1 litre of water at a p ...

Prove that one of the lines represented by ax3+bx2y+cxy2+dy3=0 will bisect the angles between the other two if (3a+c)2(bc+2cd-3ad)=(b+3d)2(bc+2ab-3ad) Source: SL Loney ...

Find the moment of inertia of a cube of side a along its diagonal. ...

Find the value of [\frac{n+1}{2}]+[\frac{n+2}{2^2}]+[\frac{n+4}{2^3}]+...+[\frac{n+2^k}{2^{k+1}}]+... sum goes to infinity... Edit: [.] is the greatest integer Function We have done something of this kind before.. ...

If a, b, c are the roots of x3+2x2+3x+3 then \left( \frac{a}{a+1}\right)^3+\left( \frac{b}{b+1}\right)^3+\left( \frac{c}{c+1}\right)^3 is equal to (Another good one i got from a student) ...