Congrats!!

Many people cleared the JEE today..congrats to em all! Further, the blog now boasts of 60 followers..so congrats to me.

Now, this question HAS a history with me..
Particle 'A' is located at (1,2,3), and particle 'B' at (-1,-2,6). A has a constant velocity V1(vector), B has V2(vector).

Find the unit vector in direction of (V2-V1), if A and B are supposed to collide somewhere in the future.

This is difficult:

A marble rolls down (from rest) from a cliff of height 5m, and then encounters a vertical drop of 1m.
Find the range of the marble on the horizontal planes...

For those of you who don't know already, marbles are solid spheres, and are quite small..

Properties that Matter:

No reples to the Sand's question??? Wassup?

Now, this is something we all can do:
Shown is a spherical shell of some conducting material, like say, Steel. The inner surface is maintained at 1000K and the outer at 2000 K.

The radius of the inner and outer spherical surfaces are 1m and 2m. Find the temperature at the spherical surface of radius 1.5m.

Sands :

Here is a method to determine the coeff. of friction b/w sand particles:

A circle of unit radius is drawn (with chalk) on the ground and sand is sprinkled from a hopper into it..the maximum height of the cone achievable thus is H.

Find the value of dU/dH (U : the coeff. of friction), in terms of H.

Solution:

Not many were able to solve the length of the cycloid...
Don't worry, i never solved this one myself!!! Had an hour of frustration before looking at the solution...

Here's my version of the solution:
If you are into center of rotation, you can easily write the velocity as a function of time:
Here, the length CP is 2RCos(90-theta), which is 2RSinQ..
Q is infact wt...so V=[2RSin(wt)]*w...as the velocity is equal to the distance from center of rotation*angular velocity..

All that remains is to integrate V(t) from 0 to 2pi/w...

No partial marking:

This is the sort of problem that you will see...someday.

The solid cylinder shown in the figure is of mass 5kgs and radius 25cm. It is kept on two rail-like planks and a force 15N is applied as shown..

What is the force of friction on the cylinder from one plank??

Cycloid:

The integration involved in the calculation of length of the involute was (after some thought), intuitive...there was little choice!!

Here's something better: the circular object rolls without slipping on a horizontal surface. The motion of the lowermost point 'P' is monitored.
The path traced by this point is called a 'cycloid'...again: find the length of the cycloid, assuming the radius of the circular body 'R'...

Maybe this will do better:

Free Counters

The last question drew little response, so this is something better (with a counter, which sucks):

This is a fixed vertical cylinder (top view), and it is connected by a thread (of length equal to the circumference of cylinder) to a ball.
Now, the ball is wound around the cylinder, keeping the string taut at all times.

The path traced by the ball is called an involute...simply speaking: find the length of the involute.

One from the good old days:

I solved this one a few weeks before the JEE...and it made quite an impact...took me approx. 20 mins to even get started...

Here'e the deal:
We have a particle and a ring, both smooth, on a horizontal plane. As shown, they are initially in contact and at rest, when the particle is given a velocity V (as shown).

Find the time in which the particle completes one full revolution inside the ring.

IIT D CYL110 quiz 1

Consider this: this problem appeared in our CYL110 (a 2nd semester chemistry course) quiz...half the CS department couldn't get it right!

This gas undergoes a reversible process s depicted in the P-V curve...the center of the circle shown is (10,10) and its radius is 5;

You know whats coming...find the maximum temperature of the gas!

Fluxes and Fields

A disc (radius R, surface charge Sigma), and a point charge Q are separated by distance x...

Do:
1)Find field at the location of the charge due to the disc.
2)Flux due to the charge's field thru the disc.
3)Learn them both...you already know (1)!

Let's Begin:

This is a fairly simple one:

Given is a uniform line charge of shape as shown. Find the value/(s) of the angle A such that the electrostatic field at the center (of the loop/arc shown ) is zero.

I'm Back...

With more than two months free ahead and virtually nothing to do, i guess i'll make an attempt to revive this blog...If you ppl have done electrostats, then leave a mesg. I am out of mechanics problems, as is evident from this problem, which i copied directly from the 100P forum..

This problem teaches a few things, and though the mechanics involved is simple, the thought process is cool:

A solid sphere rolling without slipping on a rough horizontal surface with a linear speed 21m/s collides elastically with a fixed, smooth vertical wall. Find the speed of the solid sphere after it has again started pure rolling (in the backward direction) .The radius of sphere being 1m.