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Equilibrium

Shubham Mukherjee asks:

“A ball suspended by a thread swings in a vertical plane so that its acceleration values in the extreme and lowest position are equal. Find the thread deflection angel in the extreme position?”

Answer will take some time. Visitors are requested to respond

Doubts related to Electric Dipole

Ela asks:

  1. Magnitude and direction of dipole field depends not only on distance r from centre of dipole,but also on the angle between the position vector rand the dipole moment p how?
  2. How can centres of positive and negative charge lie on same place and if both have same charge they should become neutral?

Answer:

1. The electric field at a point due to a dipole is given by

Which clearly explains the answer to your question

2. Centre of positive charge means the centre of mass of all the positive charged particles and similarly for the negative charge. If the atom or molecule is symmetric, the two centres of charge will coincide; just like the centre of mass of two concentric hollow spheres. The charges are not at the same point, but their centres of mass coincide. If they do not coincide, it will give rise to an electric dipole or a polar molecule.

Why hole is positive?

Mandeep asks:

 

“As we take a negative charge on the electron,when
electron leave there position,the left particle is
hole,my question is that why we consider hole as a
positive charge ,as a hole is a efficiency of
electron not containing any charge”

 

Answer: Hole is the deficiency (not efficiency) of an electron. It is assigned a positive charge for the sake of convenience of discussing it like a moving charge. When an electron leaves a site, the atom gets ionized and gets a positive charge. This is actually caused by the deficiency of electron. SO, we treat the vacancy of electron like a mobile positive charge. When an electron from the neighbouring atom leaves its ste and another electron fill a hole previously present, we treat it as if the hole has moved from one site to another.

Links:

The person in a Portrait always looks at me?!

Kunal Asks:

“when we look continuously into the eyes of a person in a photo frame and change our position then the person appears to follow us.why is it so?”

 

Ans: Because the portrait is inanimate and is drawn in such a way that it is looking at the spectator. So, it will seem to be looking at you when you look at it. But this will not happen in the case of a statue.

Why don’t we feel Earth’s Rotation?

Sreeda Asked:

“Why are we not feeling Earth’s rotation while it is actually happening”

Answer:

It is just like we don’t feel like moving when we are inside  a train moving with constant velocity and especially when we are not looking out of the window.

When we look out from earth, we see stars and other heavenly bodies which are very much far away and the relative change in position is very much less to be noticeable.

The most celebrated test of Earth’s rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of an iron sphere suspended 67 m from the top of the Panthéon in Paris. Because of the Earth’s rotation under the swinging pendulum the pendulum’s plane of oscillation appears to rotate at a rate depending on latitude. At the latitude of Paris the predicted and observed shift was about 11 degrees clockwise per hour. Foucault pendulums now swing in museums around the world.

Determinism, quantum theory and …. ?

Anchu Wilson asked:

It is known that the behaviour of microscopic particles and systems cannot be predicted.Like, the exact position of an electron cannot be determined ,but that we can give only a probable region where this can be found.So can this theory be applied to support (at least theoretically)the existence of parallel universes,where the lack of determinism in Quantum Theory can be applied ? Suppose in one universe something happens,the reverse happens in a parallel universe,just like the position of electron is indeterminate?

Can the theory of existence of parallel universes be refuted or proved?

 

Ans:

Such a question I have discussed elsewhere in the site already. The theory of parallel universes or multiple universes is one which comes into discussion when quantum mechanics and the theory of probability is discussed.

Schrödinger’s cat is a relevant thought experiment which can be considered in this discussion.

Imagine a cat inside a box. The box is provided with a mechanism which triggers a system which inject potassium cyanide to the cat. The box is also provided with a single atom of a radio active substance. The life period of a single atom of a radio active element varies from 0 to infinity. SO, the atom may or may or decay in a given time interval. If the atom decays, the radiation emitted will trigger the cyanide injection system and it will instantly kill the cat.

If the cat is inside the box and the box is kept closed for one hour, What is the state of the cat?

Is it dead or alive?

When after one hour we open the box and see, we will EITHER  see a DEAD  cat or a LIVE cat depending on whether the atom decayed or not.

But the probability of decaying or not decaying of the atom during the one hour are equal. Then when we are not looking at the cat, what can we say about the state of the cat?

We can say that it is the superposition of the two probabilities. But when we make an observation, only one of the probabilities become a reality.

What happens to the other probabilities?

Some say that there is a MASTER MIND which determines which of the two (or many) probabilities should become the reality. One of the many probability becomes a reality and all others collapse.

It’s right to remember one saying in this context;

“To say YES to somebody is to say NO to all others”

The another theory explaining the probability turning to reality is that, whenever we make an observation, or take a result, the universe splits into as many as the number of probabilities.

So, it’s not a Universe, but a MULTIverse.

We don’t know what actually is taking place. But it’s very thought provoking to read and think on such ideas and theories.

Here are some links which you can use for further reference.

A question from kinematics – motion in one dimension

Natasha Sehgal Asked:

“A stone is thrown in a vertically upward direction with a velocity of 5m/s. If the acceleration of the stone during its motion is 10m/s^2 in the downward direction , what will be the height attained by the stone and how much time will it take to reach there?”

Answer:

Take,

u=5m/s

a= -10 m/s2

v=0 at the topmost position

S= Hmax = ?

The eqn of motion to use
v2 – u2 = 2aS
Which gives H = 1.25 m
From the eqn
v=u + at
t= 0.5 s

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Schrodinger’s Cat in Daily Life

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