Hydrostatics:

A cuboidal block of iron (6.8g/cc) ans mass=1kg is immersed in water upto 1/2 its height.

A spring with force constant K= 1N/m presses the block from above. Non-deformed length of the spring was 50cm.

Find the normal reaction on the block (at its bottom surface).

Falling Raindrop

A raindrop, whose initial size may be considered negligible, falls from a height h and increases its size by accreting (gathering) all the mist it encounters. If the mist is of uniform density ρ and extends to the ground, report the equation of motion of the falling raindrop.

P.S.: Equation of motion refers to an equation in position, velocity and accelaration.

Click here for the solution.

Ram an RanGen

Ram has a machine which he calls RanGen (Random-Number Generator). RanGen generates random numbers b/w 0 and 1.

Ram is playing a game: He uses RanGen twice and hence gets 2 numbers 'a' and 'b'. Then he shows only 'a' to you and asks the following question: 'Is 'a' larger than 'b'??'.

If you guess the answer correctly, Ram gives you 101 Rs. Otherwise he takes 101 Rs from you. Ram is willing to play this game for ever, everytime with a new 'a' and 'b'.

Develop a scheme for guessing which will 'probably' make you rich in the long run.

Note that Ram is very kind, and will let you borrow RanGen for some time if you want.

Easy? Yes it is!

If you're good, this one should not take more than 15-20 seconds even if you don't remember any formulae.
Even that's too much.

Find the flux, of a charge q, through an infinite sheet placed at a perpendicular distance d from it.

Applying JEE knowledge:

Solutions on the way.

As promised, we're trying to provide solutions for most of the blog questions. Here's the solution to a unique SHM problem.

Only one person was able to solve this correctly, so here's a chance to learn! Its a must try for 11th class students.

Hello World

I will praise myself and say that this is a wonderful blog. We have very good questions for JEE physics here, and few (if not none) books could match this collection.http://www.blogger.com/img/blank.gif

I have been very irresponsible in the past 6 months: I have not written the solution to any problem. In many questions, I see that readers have specifically asked for solutions, and I have not replied.

In order for the blog to be more useful, I'll be posting solutions regularly now, while the other 2 authors will post new questions.
I will also post questions if I find good ones.

We will host the solutions on www.shivankergoel.blogspot.com

Lyttleton-Bondi Model for the Expansion of the Universe

In 1959, Lyttleton and Bondi suggested that the expansion of the Universe could be explained on the basis of Newtonian mechanics if matter carried a net electric charge. Imagine a spherical volume of astronomical size and radius R containing un-ionized atomic hydrogen gas of uniform density η, and assume that the proton charge e(p) = (1 + y).e, where is the modulus of the electron charge.

a) Obtain the value(expression) of y for which the electrostatic repulsion becomes larger than the gravitational attraction and the gas cloud expands.

b) Obtain an expression for the force of repulsion on an atom which is at a distance R from the centre of the spherical volume. Hence show that the radial velocity is proportional to R. Let us label the proportionality constant as H. Assume that the density is maintained constant somehow by the continuous creation of matter in space. Assume also that the value of y is quite larger than the equilibrium value calculated in (a) above and hence ignore gravity.

c) Given that at time t = 0, the volume of the Universe was Vo, obtain an expression for the volume expansion of the Universe.

Note: Experiments do not indicate a difference in the magnitudes of the electron and proton charge. Some theories regarding the nature of the fundamental forces and elementary particles also do not point to a difference. Hence the Lyttleton-Bondi model has been largely discarded by the scientific community.

Fraud

This one might be a common question i guess, but not common enough!

A uniform rod of mass 7 kg and length 120 cm is hinged at one end. A particle of mass 2 kg travelling with a speed 15 m/s collides with the rod at a distance x from the center of mass of the rod such that the reaction force at the hinge is zero.

Find x.

Click here for the solution.

Permutation and Combination:

Consider the set 'S(n)' formed by erasing digits at some (0 or more) positions of a number 'n'.

For example: if n=123, S(123)={123,12,13,23,1,2,3}.
Another one: if n=122, S(122)={122,12,12,22,1,2,2}.

Let 's' denote the sum of all elements of 'S'. Find s%9 for n=12391227.

Note:
1) '%' means remainder. 5%2=1.
Some Identities:
2) (a+b)%c=(a%c+b%c)%c
3) (a*b)%c=((a%c)*(b%c))%c.

Is it possible?

Easy, yet Interesting!

Given are 2 positively charged infinite rods of a finite charge density k.

The rods, both move parallel to their length with a speed 'v' in the same direction. Find 'v', if they are to remain in equilibrium.

Bonus question:- A particle of charge q and instantaneous position r, is moving with a velocity v. Find the magnetic field vector at a point with position vector r1.

Don't Get this Wrong!

Two bobs, tied to each other by an ideal string, lie on a smooth, frictionless horizontal table.

A sudden impulse 'J' is imparted to the bob of mass 4m. Find (x+y), if the tension in the string just after the impulse is [x(J^2)]/[yml].

Use Judge-'Impulse'