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Acceleration of right block is 2 m/s2 and that of left one is 3 m/s2. Then in the frame of the right block, the acceleration of the left block is 5 m/s2 and the acceleration of the point p is 15 m/s2. Then jumping back into the ground frame it will give 13 m/s2.

@Aakhyat Singh
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In the frame of the right block, if the left block moves by x then the thread looses by 3x and the point P moves by 3x. Thus, if the acceleration of the left block is 5m/s2 then the acceleration of the point P will be 3 times 5 that is 15 m/s^2.

In our collage we are taught Constraint Relationship but I didn't find any wiki or any problem related to it. Recently I posted a new question. As I was discussing with Brain Moehring sir I asked him about this relationship but he said that he didn't hear any thing of that kind. Is there anything called as Constraint Relationship ?

This is what is taught by our physics sir :

Constraint relationship is the relationship between tension in the string and acceleration or velocity of the block connected to it. It says that the sum of all product of tensions and velocity's (or acceleration's) in a pulley system is equal to 0.

$\displaystyle \sum T \cdot \overline{v} = 0 \text{ (or) } \displaystyle \sum T \cdot \overline{a} = 0$

The expression you have written with tension and velocity is correct because all it says is total power by tension is zero. Strings do not expand or compress like springs thus they do not store energy nor they produce heat thus they don't do any work.

The second relation is true only if the tension vector is constant, then the differentiation of the first result will give you the second one.

About the constraint relations, the relation is true only when the strings are inextensible and taut.

@Rohit Gupta
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It's ok sir. I am trying to make as many examples as possible for every one to understand it clearly. If there is any mistakes in my theory and examples part please correct it sir .

A bullet when fired at a target has its velocity decreased to $50 \%$ after penetrating $30~cm$ into it. Calculate what is the additional thickness it will penetrate before coming to rest.

I am unable to solve these problems. Can you tell any technique or ways to solve this problem and the below ones. No need to fully solve them. I just want the idea.

@Ram Mohith
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Draw a diagram, then, write equations of motion from initial position to the 30 cm and from 30cm to rest of the motion. Use the equation $v^2 = u^2 + 2aS$

@Rohit Gupta
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Thank you sir. But I came to know that we can solve this another method. The method is by using work energy theorem. sir, can you please clarify my other doubts too below.

A sand bag of mass $m$ is suspended from a long string. A bullet of mass $\dfrac{m}{20}$ moving with a horizontal velocity $v$ strikes it and gets embedded into it. Calculate the velocity gained by the bag in this process. Also calculate the fraction of energy lost in this process.

A stationary radioactive nucleus of mass $210~units$ disintegrates into an alpha particle of mass 4 units and a residual nucleus of mass 206 units. If the kinetic energy of the alpha particle be $E$ then what is the kinetic energy of residual nucleus ?

@Ram Mohith,idk whether this is a crct methd, but i guess you will have to find velocity of alpha particle and then use conservation of momentum to find velocity of residual nucleus.i.e. sqrt(8E)=206v, then Kinetic Energy=206(v^2)/2....

A person of mass $M = 90~kg$ standing on a smooth horizontal plane of ice throws a body of mass $m = 10~kg$ horizontally on the same surface. If the distance between the person and body after 10 seconds is $10~m$ then what is the kinetic energy of the person (in Joules) ?

Clouds rub each other and gets charged and when the sufficiently large potential difference is generated between Earth and clouds then the dielectric breakdown of air occurs causing lighting.

Sunlight is composed of a broad spectrum of colors. When it enters the Earth's atmosphere, blue light scatters a lot more than the warmer colors, which generally reaches the ground. Hence, when you look up outward through the atmosphere, you see blue.

Let m be the mass of an object on Earth. Then gm = weight, where g is the gravitational acceleration at the surface of the Earth. If I put this same object on the moon, then it will weigh less because the gravitational acceleration is less there. Weight can vary, but mass does not.

Special Relativity R supposedly explained why both perpendicular light beams returned to the 1881 Michaelson Morley detector at approximately the same time by declaring that east-west arm of the MM device contracted because it was in motion in the direction that the beam was sent. Question: According to SR would there not also be a time dilation that has to taken into account as well as the 'length' dilation in determining when the east-west beam arrives at the detector ?

Anyone please clear my silly doubt. I know you will laugh but let me tell.
Let in a closed circuit current i is flowing. At a point on loop q charge passing in unit time t. Let in its way a resistor comes (After that point) and it opposed the flow of charge and now the charge flowing in time t(as before) is q' on a point after the resistor. But we say that here the current is also i. Why?

Can time be negative practically ? I know that time is negative if the event started before... But i want to ask my real question. "While solving quadratic equations of time we generally come through a negative value. What does this negative value of time signifies"?

Well, when you take time = 0, that means you are starting an observation at that time instant. When the time comes negative that means it refers to the time before the starting of your observations extrapolating the conditions given after the start of the observation.

No, whenever shifting of the normal reaction to create the situation of equilibrium (rotational as well as translational) is required, the normal reaction shifts.

Consider the simple example of a large box sliding down a rough incline plane. We see that it does not topple, because Normal reaction shifts to balance the torque of friction. However, if the normal reaction has shifted to the edge of the box, and still cannot cancel the torque of friction, then the box will topple.

Also, normal reaction does not always pass through the COM (as stated above), but it always acts perpendicular to the larger of the two surfaces in contact.

@Kishore S Shenoy
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For the equations of rotational motion of the body(about COM, just for the sake of example), we have to take the torques about the specified point(About COM in our example), and thus there is no confusion.

For the equations of linear motion of a body, yes, we can just take all the forces in one direction and add them as if they are acting on a single point (and we can take that point as COM as well).Also, this addition is still vectorial addition, with the only change that we don't consider their actual point of application.

Momentum measures the quantity of motion in an object which not only depends on speed but on mass as well. That is why it is more difficult to stop a truck moving at the same speed as a car.

Electric field on the surface of a conductor has to be perpendicular to the surface only if the current is not flowing...as if electric field has a component along the surface then it will make the electrons move along the surface and current will appear..!!

I have read in some books that we prove E = 0 inside a conductor by taking all Charge rests on the surface and in some book vice-versa. How to prove both together ?

When current is flowing then the field inside the conductor is not zero. In fact the field itself is responsible for the drifting motion of the charges. therefore only in case of electrostatics net field inside a conductor can be taken as zero.

@Rajdeep Dhingra
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It is very simple to prove that net field inside a conductor under electrostatic conditions is zero. Electrostatics is the condition when charges are at rest or there is no current. If there is electric field inside a conductor then the charges in conductor will start to move and hence in electrostatics electric field can't be present inside conductor.

When a photon passes through an object, its energy may be absorbed by an atom and used to promote one of its electrons to a higher energy level. When this happens, the photon is absorbed, and light cannot pass through the material- and to us, the material appears opaque, because we cannot see what lies on the other side of the object.

In the case of transparent materials like glass, the energy required to promote an electron to a higher energy level is more than that a photon can provide. Thus, the photon is not absorbed, and can pass through the material- and to us, the material appears transparent, because we can see through the object.

@Ishan Mishra what happens when the photon is absorbed and electron goes to higher energy state?? will it stays there or jumps back to ground state? if it jumps back then again light of same energy should be emitted and the energy is actually not lost..!!

@Sachin Vishwakarma I think the answer lies in resonance..!!the molecules of the materials can vibrate and if there natural frequency of vibrations is matched with the frequency of light then the light gives its energy to the molecules and the energy is lost into the vibrations of the molecules and thus the light fades away and eventually not able to come out of the other surface..!

because we have vectors which can be added and addition of two vectors should result in a vector..!!therefore there is a need of defining a null vector.
Suppose there are two negative vectors (whose magnitudes are equal and direction is opposite to each other) and they are needed to be vectorially added then there sum should have zero magnitude and the resultant should be a vector thus null vector with arbitrary direction.

There is a difference between "zero vectors" (which is what you're talking about), and "null vectors". In ordinary vector space, there isn't much any difference, but in other vector spaces, null vectors have a norm of zero, but does not necessarily have elements that are also zero. In such spaces, "null vectors" can actually have a rich structure. See this paper as an example

@Raven Herd
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$0\widehat { i } =\quad 0\widehat { j }$ therefore when the magnitude is zero then there is no point in giving it a particular direction.

@Kartik Sharma Charge is a property of matter, some particles posses it and some don't. we obviously can't see or smell this charge..but it can be felt by another charge. That is how it was first discovered. when two materials were found to be attracting or repelling each other. Therefore we can't physically conceive the charge but can only agrees about its presence by placing another charged particle in its vicinity.

"... can only agrees about its presence by placing another charged particle in its vicinity." How do I know if "the another charged particle" is actually "charged"? Of course by again "placing another charged particle in its vicinity." and the recursion continues.

Also, what actually is positive and negative charge? How do we distinguish them?

But of course, the latter question can't be answered before the first.

@Kartik Sharma
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1) If two particles attract or repel each other both of them has to be charged.
If two bodies repel each other then both of them must be charged!!

there are two types of charges, because two types of forces ie attraction and repulsion were seen And the effect were neutralized when the two were brought in contact with each other. Thus they can add to zero as well.. Therefore scientist say that the two types of charges should be +ve and -ve. Its just a convention to take electronic charge as negative. Earlier Positive charge was defined as the charge left on a glass rod after being rubbed with silk.

@Kartik Sharma
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I know the answers though because I know the physicists - "they really don't know". As Feynman says, physicists leave the "difficult" part of understanding for other subjects. The fundamentals we have made will never be "explained", I know. But still, thoughts will be welcomed but they too will be based on some other fundamental. SO, really this is a really bad question. I am sorry.

@Kartik Sharma
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See my comments about the mental habit of using "as-if" in doing theoretical physics. Here's a thought for you: If we employ "intuitive paradigms" in trying to explain physics, isn't that already a form of axiomization? The use of such "intuitive paradigms" may be injecting or imposing unwarranted, unsupported constraints on physical behavior. We now have extremely complex mathematical apparatuses in which to describe physics, and they do work. Tell me--in practical, everyday physical terms--what is a complex vector? We "know" what a "regular vector" is, it's an arrow of some kind. It's force pushing in some particular direction--like why you fall into the pool because somebody put a force vector on your back. So, what's a "complex vector"? This is one of a great many more abstract mathematical objects used in physics that are quite hard to explain in such everyday, intuitive terms.

To put it baldly, reality in theoretical physics is far richer than any set of everyday, intuitive concepts that we can come up with. We simply cannot keep up with the abstract developments in theoretical physics fast enough. The only guide that we have is the mathematics itself.

Differential equations are still woefully inadequate to describe "all" physics. But, yes, it's a personal philosophy of mine that physical reality follows mathematical reality, even if we often can't make much sense out of it.

So, on a larger scale, I will ask my old doubt about Probability Amplitudes. Why are they used? I guess they are like "potentials(vector and scalar) in EM" by which I mean only a consequence of easing out our mathematics for science.
Although, I have got a great answer by @Michael Mendrin and I am quite satisfied, yet I'd love to read other's thoughts on this topic.

One of the best mental habits to have when dealing with theoretical physics is to use the term "as if" a lot. As in, "the electron behaves as if it's a particle or a wave", or "classical mechanical systems behave as if it wants action to be minimized". Elementary particles sometimes behave as if they possess spin, i.e. exhibit certain characteristics that are mathematically similar to classical mechanical spin. But that's where the analogy probably needs to stop there. Just because an electron or a photon behaves as if it has a spin doesn't mean that there is something actually spinning. As an example, Newton thought light could be corpuscles, which are like tiny little balls, which wouldn't be hard to imagine spinning like marbles. Then Maxwell showed that light was an electromagnetic wave, which can have wave circular polarization, a kind of a spin. Quantum photons have spin 1, an attribute which shares some mathematical similarities with both the classical and EM "spin", but physically is not like either. We know this because certain properties of light are hard to explain either classically or in EM theory. One obvious difference is that in EM theory, not all photons are circularly polarized, but in quantum physics, all photons always have spin 1.

It's actually an handicap to keep trying to find simple mechanical analogues when trying to put quantum physics on an intuitive basis. If something looks like a duck, walks like a duck, quacks like a duck, is it a duck? In much of theoretical physics, no.

@Agnishom Chattopadhyay
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Going with the "as-if" habit of thought, in the Stern-Gerlach experiment (where a beam of [single] atoms is split in passing through an inhomogeneous magnetic field), the atoms behaved as if it only had $2$ spin states, one up and one down. That is, the spin of atoms behave as if spin is quantized. When the mathematics is worked out, it ruled out the possibility of integer spins, because then there would exist a ground state beam unaffected by the magnetic field, i.e. $-1, 0, 1$, which totals up to $0$ (as per classical conservation of angular momentum). With just two spin states, the physicists were kind of forced to go with $-\frac{1}{2}, \frac{1}{2}$, which totals up to $0$. That is, the atoms were behaving "as if" it had only such spin states. This experiment was done in 1922. In 1928, some years later, Dirac, after wrestling to find any "physically sensible" solutions to the Klein-Gordon equation, a relativistic version of the Schrodinger wave equation, decided (out of desperation, really) to put some restrictions on possible solutions, which led to the development of the Dirac Equation, which solutions involves Pauli matrices. It is these Pauli matrices that abstractly give rise to half-integer spins such as $\frac {1}{2}$, thus confirming the "as if" observation in the Stern-Gerlach experiment. There is no mechanical analogue whatsoever. It cannot be explained in layman terms, only a mathematician could appreciate it, as a consequence of the Dirac Equation. Particle spin is the result of combining quantum mechanics and special relativity.

The difference between integer spin and half-integer spin particles seems like a trivial thing, but it is one of the most profound facts of all physical reality. Bosons have integer spins, while fermions have half-integer spins. A mathematical consequence of that is that two or more bosons can share the same time and space, while no two fermions can ever. This is the reason why light can cross through each other transparently, while you and I cannot so simply walk right through each other. This is the consequence of the existence of the half-integer spins.

I want to know the concept of heating of gas in an adiabatic container covered with a piston and a boxed is placed on it, now tell whether the piston will move up or down or the molar specific heat capacity will remain constant or not

If by heating you mean increasing the temperature then in adiabatic process, the temperature can be increased by doing work on the gas,
molar heat capacity in adiabatic process is zero and constant.

I dont think so, it can achieve speed upto 99.99% of speed of light and not beyond it. If we supply more energy to it the energy will increase the mass of the system. Correct me if i am wrong

@Swapnil Das
–
Tachyons are a hypothetical (proposed) particle. They haven't been (conclusively) discovered yet.
The Large Hadron Collider (LHC) once announced that they had obtained readings of a neutrino that travelled faster than the speed of light, but in 2012 scientists at CERN discovered that two technical errors occurred, which lead to the disingenuous result:

The first error was with the oscillator in the global positioning system (GPS) used to track the neutrino's position in the collider.
The second error was in the fibre cables that relays the GPS signals to the Master clock at CERN used to record the result.

Since this hiccup, they haven't declared any information about faster than light particles. So Einstein's famous 110-year old theory is still valid for all intents and purposes.

@Ishan Mishra
–
There's an important distinction to be made between "tachyons" and "super-luminal neutrinos" Neutrinos are normally found travelling at speeds less than light, and for a moment there was thought to be a counterexample to that. In contrast, tachyons always go faster than light, as per Special Relativity. Hence, neutrinos are not tachyons.

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## Comments

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TopNewestSir, can you explain how you got answer as 13 for this question. I am getting answer as 11. If possible please post the solution.

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Acceleration of right block is 2 m/s2 and that of left one is 3 m/s2. Then in the frame of the right block, the acceleration of the left block is 5 m/s2 and the acceleration of the point p is 15 m/s2. Then jumping back into the ground frame it will give 13 m/s2.

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@Rohit Gupta sir, how r u telling that wrt right block, acc of point p=15 m/s^2 ??

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@Rohit Gupta sir, now i understood it sir.Thanks a lot sir !!

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Sir, are you teaching class 11 th and 12 th IITJEE syllabus at Narayana. If yes what chapter is going on in your college in class 11 at present.

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Ok. I didn't get the idea of solving the question in relative frame.

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In our collage we are taught

Constraint Relationshipbut I didn't find any wiki or any problem related to it. Recently I posted a new question. As I was discussing with Brain Moehring sir I asked him about this relationship but he said that he didn't hear any thing of that kind. Is there anything called asConstraint Relationship?This is what is taught by our physics sir :

Constraint relationshipis the relationship between tension in the string and acceleration or velocity of the block connected to it. It says that the sum of all product of tensions and velocity's (or acceleration's) in a pulley system is equal to 0.$\displaystyle \sum T \cdot \overline{v} = 0 \text{ (or) } \displaystyle \sum T \cdot \overline{a} = 0$

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The expression you have written with tension and velocity is correct because all it says is total power by tension is zero. Strings do not expand or compress like springs thus they do not store energy nor they produce heat thus they don't do any work.

The second relation is true only if the tension vector is constant, then the differentiation of the first result will give you the second one.

About the constraint relations, the relation is true only when the strings are inextensible and taut.

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Let's contribute the wiki Constraint Relation for brilliant.

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Yes sir you are correct.

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What is meant by

Classical Mechanics?What is the difference between

Classical MechanicsandModern Physics?Is there anything called

Newtonian Physics? If there what is it ?Are the above different branches of physics ?

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https://en.wikipedia.org/wiki/Classical_mechanics

https://en.wikipedia.org/wiki/Modern_physics

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A bullet when fired at a target has its velocity decreased to $50 \%$ after penetrating $30~cm$ into it. Calculate what is the additional thickness it will penetrate before coming to rest.

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What is your doubt in this problem?

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I am unable to solve these problems. Can you tell any technique or ways to solve this problem and the below ones. No need to fully solve them. I just want the idea.

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$v^2 = u^2 + 2aS$

Draw a diagram, then, write equations of motion from initial position to the 30 cm and from 30cm to rest of the motion. Use the equationLog in to reply

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A sand bag of mass $m$ is suspended from a long string. A bullet of mass $\dfrac{m}{20}$ moving with a horizontal velocity $v$ strikes it and gets embedded into it. Calculate the velocity gained by the bag in this process. Also calculate the fraction of energy lost in this process.

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A stationary radioactive nucleus of mass $210~units$ disintegrates into an alpha particle of mass 4 units and a residual nucleus of mass 206 units. If the kinetic energy of the alpha particle be $E$ then what is the kinetic energy of residual nucleus ?

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@Ram Mohith,idk whether this is a crct methd, but i guess you will have to find velocity of alpha particle and then use conservation of momentum to find velocity of residual nucleus.i.e. sqrt(8E)=206v, then Kinetic Energy=206(v^2)/2....

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A person of mass $M = 90~kg$ standing on a smooth horizontal plane of ice throws a body of mass $m = 10~kg$ horizontally on the same surface. If the distance between the person and body after 10 seconds is $10~m$ then what is the kinetic energy of the person (in Joules) ?

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Is the Universe finite?

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The observable universe is finite.

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$\LARGE\text{How lightning works?}$ Image source: Nasa

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Clouds rub each other and gets charged and when the sufficiently large potential difference is generated between Earth and clouds then the dielectric breakdown of air occurs causing lighting.

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Why the sky is blue?

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Sunlight is composed of a broad spectrum of colors. When it enters the Earth's atmosphere, blue light scatters a lot more than the warmer colors, which generally reaches the ground. Hence, when you look up outward through the atmosphere, you see blue.

See Rayleigh Scattering

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What is the difference between weight and mass? why weight changes but mass doesn't?

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Weight is a force, mass is not.

Let m be the mass of an object on Earth. Then gm = weight, where g is the gravitational acceleration at the surface of the Earth. If I put this same object on the moon, then it will weigh less because the gravitational acceleration is less there. Weight can vary, but mass does not.

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Special Relativity R supposedly explained why both perpendicular light beams returned to the 1881 Michaelson Morley detector at approximately the same time by declaring that east-west arm of the MM device contracted because it was in motion in the direction that the beam was sent. Question: According to SR would there not also be a time dilation that has to taken into account as well as the 'length' dilation in determining when the east-west beam arrives at the detector ?

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i want to know that what is the effect of back emf induced in a circuit with inductor?

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Inductors don't want the current to change through them instantly, therefore, they generate this emf to oppose the change in it.

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Collision Gallore Please, someone post the solution to the above problem. @Rohit Gupta Sir, @Michael Mendrin Sir,@Ishan Dasgupta Samarendra . Thanks

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Anyone please clear my silly doubt. I know you will laugh but let me tell. Let in a closed circuit current i is flowing. At a point on loop q charge passing in unit time t. Let in its way a resistor comes (After that point) and it opposed the flow of charge and now the charge flowing in time t(as before) is q' on a point after the resistor. But we say that here the current is also i. Why?

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Because with resistance electric field will also vary to keep the current same.If resistance increases then the electric field will also increase.

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Can time be negative practically ? I know that time is negative if the event started before... But i want to ask my real question. "While solving quadratic equations of time we generally come through a negative value. What does this negative value of time signifies"?

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Well, when you take time = 0, that means you are starting an observation at that time instant. When the time comes negative that means it refers to the time before the starting of your observations extrapolating the conditions given after the start of the observation.

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Does Normal Reaction act always on the centre of mass?

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Hi, @Kishore S Shenoy

No, whenever shifting of the normal reaction to create the situation of equilibrium (rotational as well as translational) is required, the normal reaction shifts.

Consider the simple example of a large box sliding down a rough incline plane. We see that it does not topple, because Normal reaction shifts to balance the torque of friction. However, if the normal reaction has shifted to the edge of the box, and still cannot cancel the torque of friction, then the box will topple.

Also, normal reaction does not always pass through the COM (as stated above), but it always acts perpendicular to the larger of the two surfaces in contact.

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So, can we take that all forces act at CM when we balance forces linearly?

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For the equations of linear motion of a body, yes, we can just take all the forces in one direction and add them as if they are acting on a single point (and we can take that point as COM as well).Also, this addition is still vectorial addition, with the only change that we don't consider their actual point of application.

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What is physical meaning of momentum ? What it's significance ?

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Momentum measures the quantity of motion in an object which not only depends on speed but on mass as well. That is why it is more difficult to stop a truck moving at the same speed as a car.

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@Rohit Gupta Sir and @Michael Mendrin sir, please see this note and help. Thanks

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In a conductor why do field lines come out radially?

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Electric field on the surface of a conductor has to be perpendicular to the surface only if the current is not flowing...as if electric field has a component along the surface then it will make the electrons move along the surface and current will appear..!!

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Oh okay thanks.

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In a conductor why does field lines come out radially?

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Because if they will come out at an angle then there will be two components.

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@Michael Mendrin Can you explain polarization and di/para/ferro/ferri -magnetism(and Lande's g-factor) quantum mechanically?

Also, it would be great if you first explain the angular momentum in QM.

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What was Rabi Molecular Experiment actually?

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When does two positive charges attract.

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Two positive charged bodies may attract if the process of induction is dominated.!!

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Why should Magnetic Field be velocity dependent but electric field not? Is there a field that unifies both things at once?

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Because only moving charges produce magnetic field. But E-field can be produced by both moving and rest charges. Concept of EM waves unifies both.

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what is a solenoid

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Solenoid is basically a coil wrapped tightly around generally a cylindrical rod

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What came first , physics or mathematics and what was created to support the other?

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Mathematics is completely independent of physics. Mathematics is called as the language of science. So mathematics is needed to express physics.

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I have read in some books that we prove E = 0 inside a conductor by taking all Charge rests on the surface and in some book vice-versa. How to prove both together ?

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When current is flowing then the field inside the conductor is not zero. In fact the field itself is responsible for the drifting motion of the charges. therefore only in case of electrostatics net field inside a conductor can be taken as zero.

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But how to prove this in Electrostatic Conditions ?

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@Rohit Gupta

Sir please replyLog in to reply

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By proving that charges on a conductor would better reside on the surface since that would lower the potential

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Why some objects are transparent and some are opaque???

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When a photon passes through an object, its energy may be absorbed by an atom and used to promote one of its electrons to a higher energy level. When this happens, the photon is absorbed, and light cannot pass through the material- and to us, the material appears opaque, because we cannot see what lies on the other side of the object.

In the case of transparent materials like glass, the energy required to promote an electron to a higher energy level is more than that a photon can provide. Thus, the photon is not absorbed, and can pass through the material- and to us, the material appears transparent, because we can see through the object.

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@Ishan Mishra what happens when the photon is absorbed and electron goes to higher energy state?? will it stays there or jumps back to ground state? if it jumps back then again light of same energy should be emitted and the energy is actually not lost..!!

@Sachin Vishwakarma I think the answer lies in resonance..!!the molecules of the materials can vibrate and if there natural frequency of vibrations is matched with the frequency of light then the light gives its energy to the molecules and the energy is lost into the vibrations of the molecules and thus the light fades away and eventually not able to come out of the other surface..!

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Why do we actually have null vectors?

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because we have vectors which can be added and addition of two vectors should result in a vector..!!therefore there is a need of defining a null vector.

Suppose there are two negative vectors (whose magnitudes are equal and direction is opposite to each other) and they are needed to be vectorially added then there sum should have zero magnitude and the resultant should be a vector thus null vector with arbitrary direction.

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There is a difference between "zero vectors" (which is what you're talking about), and "null vectors". In ordinary vector space, there isn't much any difference, but in other vector spaces, null vectors have a norm of zero, but does not necessarily have elements that are also zero. In such spaces, "null vectors" can actually have a rich structure. See this paper as an example

On Spinors and Null Vectors

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Why can't we have any particular direction , and not this 'arbitrary' direction if after all it exists only to complete the mathematics of it?

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$0\widehat { i } =\quad 0\widehat { j }$ therefore when the magnitude is zero then there is no point in giving it a particular direction.

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@Rohit Gupta sir I'm studying image theory can I get to know more about it??

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Aditya what do you know till now and what further you want to know..please elaborate your question.

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Can a ring can contain steady charge.

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I hope Yes!!

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But energy of ring configuration is not finite.

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Can charge exist without mass

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Nope charge is a property of matter..!!

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What is a charge? I have never got a satisfying answer for this question.

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@Kartik Sharma Charge is a property of matter, some particles posses it and some don't. we obviously can't see or smell this charge..but it can be felt by another charge. That is how it was first discovered. when two materials were found to be attracting or repelling each other. Therefore we can't physically conceive the charge but can only agrees about its presence by placing another charged particle in its vicinity.

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"... can only agrees about its presence by placing another charged particle in its vicinity." How do I know if "the another charged particle" is actually "charged"? Of course by again "placing another charged particle in its vicinity." and the recursion continues.

Also, what

actuallyis positive and negative charge? How do we distinguish them?But of course, the latter question can't be answered before the first.

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If two bodies repel each other then both of them must be charged!!

there are two types of charges, because two types of forces ie attraction and repulsion were seen And the effect were neutralized when the two were brought in contact with each other. Thus they can add to zero as well.. Therefore scientist say that the two types of charges should be +ve and -ve. Its just a convention to take electronic charge as negative. Earlier Positive charge was defined as the charge left on a glass rod after being rubbed with silk.

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To put it baldly, reality in theoretical physics is far richer than any set of everyday, intuitive concepts that we can come up with. We simply cannot keep up with the abstract developments in theoretical physics fast enough. The only guide that we have is the mathematics itself.

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Is all of physics merely a bunch of differential equations? And all of the mathematics an attempt to solve those?

*This is actually a personal thought.

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Differential equations are still woefully inadequate to describe "all" physics. But, yes, it's a personal philosophy of mine that physical reality follows mathematical reality, even if we often can't make much sense out of it.

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So, on a larger scale, I will ask my old doubt about Probability Amplitudes. Why are they used? I guess they are like "potentials(vector and scalar) in EM" by which I mean only a consequence of easing out our mathematics for science. Although, I have got a great answer by @Michael Mendrin and I am quite satisfied, yet I'd love to read other's thoughts on this topic.

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What is spin, really?

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One of the best mental habits to have when dealing with theoretical physics is to use the term "as if" a lot. As in, "the electron behaves as if it's a particle or a wave", or "classical mechanical systems behave as if it wants action to be minimized". Elementary particles sometimes behave as if they possess spin, i.e. exhibit certain characteristics that are mathematically similar to classical mechanical spin. But that's where the analogy probably needs to stop there. Just because an electron or a photon behaves as if it has a spin doesn't mean that there is something actually spinning. As an example, Newton thought light could be corpuscles, which are like tiny little balls, which wouldn't be hard to imagine spinning like marbles. Then Maxwell showed that light was an electromagnetic wave, which can have wave circular polarization, a kind of a spin. Quantum photons have spin 1, an attribute which shares some mathematical similarities with both the classical and EM "spin", but physically is not like either. We know this because certain properties of light are hard to explain either classically or in EM theory. One obvious difference is that in EM theory, not all photons are circularly polarized, but in quantum physics, all photons always have spin 1.

It's actually an handicap to keep trying to find simple mechanical analogues when trying to put quantum physics on an intuitive basis. If something looks like a duck, walks like a duck, quacks like a duck, is it a duck? In much of theoretical physics, no.

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Thanks.

More questions: What does it mean to have spin 1/2? 1/2 of what?

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as ifit only had $2$ spin states, one up and one down. That is, the spin of atoms behave as if spin is quantized. When the mathematics is worked out, it ruled out the possibility of integer spins, because then there would exist a ground state beam unaffected by the magnetic field, i.e. $-1, 0, 1$, which totals up to $0$ (as per classical conservation of angular momentum). With just two spin states, the physicists were kind of forced to go with $-\frac{1}{2}, \frac{1}{2}$, which totals up to $0$. That is, the atoms were behaving "as if" it had only such spin states. This experiment was done in 1922. In 1928, some years later, Dirac, after wrestling to findany"physically sensible" solutions to the Klein-Gordon equation, a relativistic version of the Schrodinger wave equation, decided (out of desperation, really) to put some restrictions on possible solutions, which led to the development of the Dirac Equation, which solutions involves Pauli matrices. It is these Pauli matrices that abstractly give rise to half-integer spins such as $\frac {1}{2}$, thus confirming the "as if" observation in the Stern-Gerlach experiment. There is no mechanical analogue whatsoever. It cannot be explained in layman terms, only a mathematician could appreciate it, as a consequence of the Dirac Equation. Particle spin is the result of combining quantum mechanics and special relativity.The difference between integer spin and half-integer spin particles seems like a trivial thing, but it is one of the most profound facts of all physical reality. Bosons have integer spins, while fermions have half-integer spins. A mathematical consequence of that is that two or more bosons can share the same time and space, while no two fermions can ever. This is the reason why light can cross through each other transparently, while you and I cannot so simply walk right through each other. This is the consequence of the existence of the half-integer spins.

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Ya, my doubt too!

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Hi guys, I had a doubt about friction. My note is here: https://brilliant.org/discussions/thread/i-have-a-problem-with-friction/

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Is there any possibility of Grand Unified Theory?

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I want to know the concept of heating of gas in an adiabatic container covered with a piston and a boxed is placed on it, now tell whether the piston will move up or down or the molar specific heat capacity will remain constant or not

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If by heating you mean increasing the temperature then in adiabatic process, the temperature can be increased by doing work on the gas, molar heat capacity in adiabatic process is zero and constant.

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Can any system travel faster than light ?

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No

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A hypothesis is based on tachyons for this. I dnt believe it.

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I dont think so, it can achieve speed upto 99.99% of speed of light and not beyond it. If we supply more energy to it the energy will increase the mass of the system. Correct me if i am wrong

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The discovery of tachyons makes me doubt.

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The first error was with the oscillator in the global positioning system (GPS) used to track the neutrino's position in the collider. The second error was in the fibre cables that relays the GPS signals to the Master clock at CERN used to record the result.

Since this hiccup, they haven't declared any information about faster than light particles. So Einstein's famous 110-year old theory is still valid for all intents and purposes.

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It sounds awkward when one sees an Einstein face asking a question that goes against his theory! :P

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