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Lets start a marathon..with a very good question. 
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#1
Mar2713, 09:04 AM

P: 20

A very good question which i solved a couple of hours back..
Theres a figure i have given. Its a uniform solid cylinder of Radius R(say) and Mass M(say), Which is free to rotate about a fixed horizontal axis O and passes through Centre of the given cylinder.At One end lets say theres an spring(assume its ideal) of force constant say some K is fixed and other end is hinged to the cylinder at point A. Distance OA is half of the radius of the base of cylinder (simply R/2). A thread(obviously inextensible) is wrapped round the cylinder and passes over a smooth pulley(neglect the radius of pulley though). A block of equal mass M (remember mass of cylinder is also M) and having crosssectional area A is suspended from free end of the thread. The block is partially immersed in a nonViscous liquid of density ρ. Say if in equilibrium, spring is horizontal and line OA is vertical. Find the frequency of small oscillations in the whole system. i got the answer as.. 1/2∏ √((K + 4Aρg)/6M) check it out and solve. After you solve this question. You have to post the solution along with another question. And again once the other guy solves your question, he posts the solution along with another question and the marathon goes on and on. Lets see how big its getting 


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