A hollow straight tube of length l and mass m can turn freely about its centre (fixed) on a smooth horizontal table. Another smooth uniform rod of same length and mass is fitted into the tube so that their centres coincide. The system is set in motion with an initial angular velocity ω0. The angular velocity of the rod at an instant when the rod slips out of the tube is:
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a
ω03
b
ω02
c
ω04
d
ω07
answer is D.
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Detailed Solution
Initial angular momentum about O isL1 = 2(ml212)ω0 = ml26ω0Final angular momentum about O isLf = Iω = [ml212+(ml212+ml2)]ω = 76ml2ωAngular momentum will be conservedLi = Lf or ω = ω07