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## SPEED OF DARKNESS?

IN PHYSICS I OFTEN GET STRUCK OF A QUESTION OF NOT A SINGLE TEACHER OR MY FRIENDS COULD ANSWER ME THE QUESTION IS THAT

“IF SPEED OF LIGHT IS 3 x 108 METRE PER SEC, THAN WHAT IS THE SPEED OF DARKNESS????….”

## Mirror Mirror Relativity

Can you see your image when you are travelling at the speed of light?

Einstein’s Theory of relativity says:”The Laws of Physics are the same in any Inertial Frame of Reference.”

## Motion in a vertical circle and conservation of energy

A stone  tied to a string of length l is whirled around a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at the lowest position and has a speed u. What is the magnitude of change in its velocity as it reaches a position where the string is horizontal?

Let’s assume that the potential energy at the lowest position be zero. So, when the string is horizontal, the stone has risen by a vertical height l, the length of the string which is also the radius of the vertical circle.

If v is the magnitude of velocity at the horizontal position, then according to the law of conservation of energy,

KE+PE at the lowest position = KE+PE at the horizontal position

$\frac{1}{2}mu^{2}=\frac{1}{2}mv^{2}+mgl$

From the equation above, v-u can be calculated.

$v=\sqrt{u^{2}-2gl}$

The following links will help you for deeper understanding and you can browse through some solved problems from the topic too.

## Collection of Problems received from Class 12 Physics

These problems were posted by Geena. Hope that we will be able to post the answers to these questions soon; each in a separate post. By the time visitors can attempt to post their answers as comments to this post. (Only selected posts will be published)

Please note that the answers are not published until the Physics teachers are not satisfied with the answers. So, please be patient to get the correct answers rather than approximations in a haste.

If you want real time answers to your queries by a group of Physics Lovers, you can post them at the Physics Fans group with facebook at https://www.facebook.com/groups/askphysics/

1. A series battery of 10 lead accumulators each of emf 2 V and internal resistance 0.25 ohm is charged by a 220 V D.C. mains to limit the charging current a resistance of 47.5 ohm is used in series in the charging circuit. What is a) the power supplied by the mains and b) power dissipated as heat? Account for the difference of powers is (a) and (b).
2. A potentiometer wire has a length L and a resistance Ro. It is connected to a battery and
a resistance combination as shown. Obtain an expression for the potential drop per unit length of this potentiometer wire. What is the maximum emf of a ‘test cell’ for which one can get a ‘balance point’ on this potentiometer wire? What precaution should one take, while connecting this ‘test cell’ , in the circuit?
3. A cell, of emf 4 V and .internal resistance 0.5 Ω, is connected across a load of resistance (i) 7.5 Ω, (ii) 11.5 Ω. Calculate (i) the ratio of the differences in the emf of the cell and the potential drop across the load, and (ii) the ratio of the currents in the two cases.
4. In the figure shown, calculate the total flux of the electrostatic field through the spheres S1 and S2 The wire, AB, shown here, has a linear charge density, λ given by λ = kx where x is the distance measured along the wire, from the end A.
5. A straight wire, of length L, carrying a current I, stays suspended horizontally in mid air in a region where there is a uniform magnetic field B . The linear mass density of the wire is λ. Obtain the magnitude and direction of this magnetic field.
6. Two cells of same emf E, but different internal resistance rl and r2 are connected to an external resistance R as shown. in the figure. The voltmeter V reads zero. Obtain an expression for R in terms of rl and r2. Calculate the voltage across the cell of internal resistance r2. (Assume that the voltmeter V is of infinite resistance).
7. A galvanometer with a coil of resistance 120 ohm shows full scale deflection for a current of 2.5 mA How will you convert the galvanometer into an ammeter of range 0 to 7.5 A ? Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more than the actual current in the original circuit? Justify your answer.
8. Figure shows a bar magnet M falling under gravity through an air cored coil C. Plot a graph
showing the variation of induced e.m.f (E) with time (t). What does the area enclosed by the
E – t curve depict ?
9. The electron in the hydrogen atom circles around the proton with a speed of 2.18 x 106 m/s in an orbit of radius 5.13 x 10 -11 m. What magnetic field does it produce at the centre?
10. A proton moves with a speed of 7.45 x 105 m/s directly towards a free proton originally at rest. Find the distance of the closest approach for the two protons. (Given: mass of proton = 1.67 x 10–27 kg and e = 1.6 x 10 –19 C)
11. Figure (a), (b) and (c) show three a.c. circuits in which equal currents are flowing. If the frequency of emf be increased, how will the current be affected in these circuits? Give reason for your answer.

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## Which books should be referred for IIT JEE ?

We have received hundreds of questions on the above subject. As the questions continue to pour in, we found it necessary to create a post on it.

IIT JEE is an entrance exam of international repute and IITs are considered at par with MIT by many. So, if you are an IIT aspirant, it is very much essential to prepare well in advance.

Know the fundamentals

Knowing the fundamentals is the first step. Learn your daily lessons well. In learning Physics, “Questioning Every Answer is more important than Answering Every Question”

Whenever you learn a new concept, try to get all the doubts clarified. Ask doubts and questions to your teachers. (If they don’t answer you satisfactorily, post them at www.askphysics.com )

Observe your surrounding and try finding examples on what you have learnt. The syllabus and books give you a framework on what to study; but don’t just limit your studies on books and syllabus. Search related information from real life and other sources of reference.

RECOMMENDED BOOKS FOR IIT JEE PREPARATION

The very first book you cannot avoid is the NCERT TEXT BOOK for class XI and XII

These books are designed after thorough research and the exercises are carefully added. Be sure to solve all the exercises including the Additional Exercises

Here are some of the Books you can refer for practicing for IIT JEE

1. Concepts of Physics (by H C Verma)
2. Fundamentals of Physics (by Resnick, Hallidey)
3. University Physics (Zemansky)
4. Problems in Physics (IE Irodov)

By the by, having too much books will be a hindrance. It is better to start with the NCERT books and after mastering all the exercises take up Resnick Hallidey and after clarifying the concepts take up Problems from H C Verma’s concepts of Physics and then go on to IRODOV if time allows.

Wish you all the best.

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## Why protons attract inside a nucleus?

What is the reason for proton- proton attraction inside the nucleus according to nuclear physics? (Sanjeev Asked)

Answer: Inside the nucleus where the nucleons are very close to each other, the force which holds them together is the nuclear force, which is the strongest force in nature. The electrostatic force between protons is negligibly small compared to the nuclear force. But the nuclear force is of a very short range, 10^-15 m.

The nuclear force is charge independent, i.e; the nuclear force between proton and proton, proton and neutron as well as neutron and neutron are almost the same.

Yukawa’s meson theory suggest that the nuclear force is an exchange force. The nucleons are bound because of constant exchange of the mesons.

The nuclear force is only felt among hadrons. At small separations between nucleons (less than ~ 0.7 fm between their centers) the force becomes repulsive, which keeps the nucleons at a certain average separation, even if they are of different types. At distances larger than 0.7 femtometer (fm) the force becomes attractive between spin-aligned nucleons, becoming maximal at a center-center distance of about 0.9 fm. Beyond this distance the force drops essentially exponentially, until beyond about 2.0 fm separation, the force drops to negligibly small values.

At short distances (less than 1.7 fm or so), the nuclear force is stronger than the Coulomb force between protons; it thus overcomes the repulsion of protons inside the nucleus.

However, the Coulomb force between protons has a much larger range due to its decay as the inverse square of charge separation, and Coulomb repulsion thus becomes the only significant force between protons when their separation exceeds about 2 to 2.5 fm.

(There are many terms introduced in the explanation. You can discuss them as comments for obtaining further details, if required)

Reference:

## Is the acceleration due to gravity different in south pole and north pole

“Is the acceleration due to gravity different in south pole and north pole?”

As per theory, acceleration due to gravity changes with altitude, depth and latitude.

If we consider that the variation of g with latitude is caused by rotation of earth only, then the value of g will be same for both north pole and south pole.

But, the change in the value of acceleration due to gravity with latitude is caused by the shape of earth too. So it depends your distance from the centre of earth when you are at north pole or south pole.

For calculations the polar radius is taken same at North as well as south pole. So, value of g can be taken the same for both poles.

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