CM:

This is a solar panel (believe it). Your company proposes to set it up in some remote desert. You have a plan:

You want to have the panel balanced on the tip of a thin vertical tower (!!!). Give the equation of the tower wrt. the given coordinate axes.

(I kid you not. I'm not making this stuff up!)

This is One-of-the-Best:

A point source of light radiates monochromatic light with an intensity 1 Cd.

Now, take a convex lens (f=10cm) and place this source at its focus. (You have one focus left.)

Simple, whats the intensity at the other focus?

Assume lens is too small..:P

Textbook:

This is a fairly standard problem, which most of you might have seen.

A flexible cord is placed on a quarter-circular surface (radius=1m). With what speed does the bottom of the chain hit the ground?

A Flyball-Governer:

The diagram shown is that of a "FLYBALL GOVERNOR". It consists of 2 bearings 'A' and 'B'. 'A' is fixed while 'B' can slide up and down the rod.

The bearings are attached to 2 massive balls (assume 1000kg balls). The balls are spinning with a speed 10m/s.

The speed of the balls can be 'governed' by adjusting the distance between the bearings.
The distance is reduced (slowly and smoothly) form 1m to 1/2m.

What is the new speed of the balls?


NOTE: ignore the '3m' shown in diagram.

Open your third eye:

Find out unequal positive integers a,b,c,d,e,f,g,h such that
(a+b+c+d+e+f+g+h)^2=
a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3

There is man named 'Mabu' who switches on-off the lights along a corridor at our
university. Every bulb has its own 'toggle' switch that changes the state of the light. If the light is off, pressing the switch turns it on. Pressing it again will turn it off.
Initially each bulb is off.
He does a peculiar thing. If there are 'n' bulbs in the corridor, he walks along the corridor back and forth 'n' times. On the 'i'th walk, he toggles only the switches whose position is divisible by 'i'.
He does not press any switch when coming back to his initial position.
The 'i'th walk is defined as going down the corridor (doing his peculiar thing) and coming back again.
Assume n=44,100.
Determine the final state of the last (44,100th) bulb. Is it on or off?

The 1st, 2nd and 3rd quadrants of the Cartesian Coordinate plane are given a charge density 1C/m^2.

What work has to be done in taking a unit positive charge from z=1 to z=3?

I Love This One:

A hoop (mass 'm') is placed on a smooth horizontal surface as shown. A particle (mass '2m') is initially at the position shown, then it is given a velocity 3m/s, tangential to the hoop.

Radius R=(1/pi)m.

The motion that follows is quite complex, so is your analysis.

Find the time in which the particle completes 1 complete revolution inside the hoop.

Clarification:

Here's a little argument as to why the charge density increases as the radius decreases:

Consider two conducting spheres connected by a wire.
Let us give the 'system' a charge Q. This charge will distribute itself between the two spheres.

Finally, let the charges on the two spheres be q1 and q2. Can you prove that:

q1/(4*pi*r1^2) is greater than q2/(4*pi*r2^2)? This implies that the charge density is higher on the smaller sphere.

I am trying to remember some 'good' maths problems, but I am having a tough time.
Till then, try this:

Charge 'Q' is given to a hollow conducting cone. Find the electric field at the center of the base of the cone.

Assume any parameters that you need.