rotating crackers

Classical Mechanics Level pending

the PROBLEM is : a diwali cracker which works on principle of thrust.the cracker is hinged at the center .initial mass of the cracker is M and radius is R. the cracker is in the shape of a spiral whose turns are too close that we can assume it to be a disc.the gases are ejected tangentially from the end of the cracker with a constant velocity V w.r.t the cracker. find the angular velocity of the cracker when the mass remains half.

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