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A MIND BOGGLING PHYSICS QUESTION!!!

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Hey there! This is your boffin daydreamer.  Do you like solving challenging physics questions? Then try this! Question 1: A cylinder is placed on a puddle of water. Initially the system is in equilibrium. A balloon, filled with liquid of density ‘Rho’ is dropped from a height ‘h’, from the cylinder, into the cylinder. Let the cylinder sink into the water by a distance ‘d’ as the balloon bounces back to a height ‘h/2’. Assuming that the ballon bursts as soon as the cylinder sinks by distance ‘d’ and only 20% of the liquid manages to fill inside the cylinder, find the initial volume of liquid inside the balloon so that even after the balloon has burst, the cylinder is still immersed by the depth ‘d’. (Mass of cylinder = M, density of water = (Rho)l) All the Best!! Solution: Question 2: A hollow bead (Mass M; Outer Radius R; Inner radius r) is placed along an infinitely long charged rod of linear charge density ‘L’.   Mercury, which is charged with a volumetric charge distribution ‘Rho’,