THERE IS A SPHERE WITH A CAVITY ROTATING AT AN ANGULAR SPEED w .INSIDE THE CAVITY A SOURCE OF POWER P IS KEPT ......THE COEFFICIENT OF VOLUME EXANSION IS B ......AND SPECIFIC HEAT CAPCITY IS

C(ASSUMING NEGLIGIBLE WORK DONE AGAINST ELASTIC AND ATMOSPHERIC FORCES) FIND THE RATE OF CHANGE OF ANGULAR ACCELARATION......REST MINUTE DETAILS ARE IN THE DIAGRAM

TIME : 4 DAYS (ON SUNDAY  I WILL POST THE ANSWER AND HINT)

I'll just give my method: (Not solving... too lazy )

Power of the source is P

Let the mass of the object be some m.

Then, in a time t, heat supplied = Pt = mC

or .

Now, change in volume of the cylinder =

Hence find change in radius.

Now, there is no external torque on the system, hence,

We can calculate the two moment of inertias using the standard result, and also using the change in volume that we deduced previously.

Using that, you get as a function of time. Differentiate it twice wrt time to get ur result :)

oye seriously yaar.......look dude jab problem create karte hain.....there shud be a point behind it........is problem main ther's nothing besides complication, complication , and complication........evn i can create a problem wherin i can say that i have a disc on an incline plane which is heated at a given rate and simultanously the angle of inclination is changing in such a way that the angular accn. of the plane is @ so finally find the distance covered as a function of time.....some one might evn hav the patience to hold his nerve and solve the complicated differential eqn.s and get the answer.....but ther's no pt in it........relax maan this is JEE and wen they give a prob. they wanna test ur concepts.....not ur ability to solve complex differential eqn. or sumthing.........

so jus. take a chill pill and relax......

aim for stars ..u land on moon ..

wanna crack jee @pramod ..think beyond it !!

oye yaar budokai....im not against targetting stars........target the stars......i never held u frm doing so......but why target sumthing thats gonna lead u nowhere........as i said before i cud make a masala of a problem by including a mixture of a lot of concepts........from heat....from mechanics........from modern physics.....from optics.......from Quamtum mechanics evn.....but wats the pt in it if its gonna lead u nowhere........take for eg the problem that i posted earlier.....the inclined plane wall....lets say that it is radio active also.........itll be very interesting but ull waste one whole day solving compluicated differential eqn.s..........ull become an expert in solving maths instead of becoming an expert in physics yaar(my teaches favourite line).........so target a star.........but donot mistake a black-hole to be a star....orelse ull get sukd in and by the time u get out(if u were powerful enuff) ull find a lot of time wasted..............

sorry dude ..

i respect ur words..