Recent content by einstone

So, is U a class according to Neumann–Bernays–Gödel set theory ? I reckon it is. How about G={ X | X is a set } ? Does it fit in with the Zermelo-Fraenkel set theory? Here ,too, P(G) belongs to G & also, every element of P(G) belongs to G. Unlike with U , we have obvious...

U is the set of all power sets in the world - it contains, for instance, P(R) (where R is the set of real numbers) ,P(P(R)) &c. U contains elements other than P(U) - P(R),P(The set of all continuous functions) to mention some of the innumerable possibilities.This makes P(U)...

A Paradox ? Consider the following set - ( P(Y) denotes the power set of Y) : U = { X | There exists a set Y such that X = P(Y) } Clearly , U exists :) & is non-empty. Hence, P(U) belongs to U (by the very definition of U). This contradicts the result by Cantor that the power...

Are the laws of thermodynamics compatible with the theory of relativity? I'm doubtful about irreversibility & the concept of an infinitely slow process. Please help me. I am,with great respect, Einstone.

Methinks your friend meant that quantum mechanical models are for atomic phenomena & are to be applied when the action is of the order of Planck's constant. Regards, Einstone.

I'm not sure if physics deals in questions such as 'why unlike charges attract' . We can 'explain' a phenomenon only in terms of a few basic experimental results which are formulated mathematicallly. One can't have an absolute answer to a 'Why' without assuming the truth of something else. The...

The first integrand varies as 1/sqrt(x) near zero ( I checked what the expression becomes for small values of x by means of the power series expansion.) .So, the integral will converge or diverge according as the integral of 1/sqrt(x).It converges. Similarly,to put in awful...

The above formula applies only to uniformly accelerating bodies. When acceleration & distance are interdependent , the corresponding differential equation needs to be solved. You'll find these tricks in any resource on the motions of planets. But accelerating charges radiate...

If the question is about the volume of the solid of revolution, the answer is negative except in case of x=1 to x=inf. The second question is answerable in terms of order relations only in the regions where the functions don't have zeroes.( It's easy to construct an example where the...

Unlike the total momentum,the total energy is not conserved during this inelastic collision. Regards, Einstone.

I wonder about the extent to which mathematics has influenced the development of physics. Could the physics have been different if the development of mathematics had taken a different path? For, not all physicists can develope new mathematical techniques which may be required to study a...

Do you know that the acceleration of the centre of mass of a rigid body is equal to (The net extenal force)/The total mass ? ( That's what the hint implied). If you apply this theorem to the blade,the force will be (Total mass)*( The acc. of the centre of mass, which is L/2 into the...

Constringence is the dispersivity (also known as Abbe number) of a material. For the exact definition, visit any website with information on optics-try [PLAIN]www.explore-physics.com[/URL] . Regards...

Answer to Question1: Put theta=arctan(dy/dx) & phi=arctan(y/x) in the formula you've got. But why not use polar coordinates? That'd solve all the problems. I'm,with great respect...

First find the acceleration of the system (=Tension/the total mass - mu* g)(the acceleration due to gravity). Therefore,if you know the mass of the sled pulled by rope 2,the problem is solved. In the other question, the tension in the thread is mass2*g , which equals the centripetal...