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physics

mechanics

Easy

Question

$A space h o l l o w space s t r a i g h t space t u b e space o f space l e n g t h space l space a n d space m a s s space m space c a n space t u r n space f r e e l y space a b o u t space i t s space c e n t r e space left parenthesis f i x e d right parenthesis space o n space a space s m o o t h space h o r i z o n t a l space t a b l e. space A n o t h e r space s m o o t h space u n i f o r m space r o d space o f space s a m e space l e n g t h space a n d space m a s s space i s space f i t t e d space i n t o space t h e space t u b e space s o space t h a t space t h e i r space c e n t r e s space c o i n c i d e. space T h e space s y s t e m space i s space s e t space i n space m o t i o n space w i t h space a n space i n i t i a l space a n g u l a r space v e l o c i t y space omega subscript 0 space space. space T h e space a n g u l a r space v e l o c i t y space o f space t h e space r o d space a t space a n space i n s tan t space w h e n space t h e space r o d space s l i p s space o u t space o f space t h e space t u b e space i s colon$

$ω_{0} / 3$
$ω_{0} / 2$
$ω_{0} / 4$
$ω_{0} / 7$

The correct answer is: $ω_{0} / 7$

$L subscript i equals 2 open parentheses fraction numerator m l squared over denominator 12 end fraction close parentheses omega subscript 0 equals fraction numerator m l squared over denominator 6 end fraction omega subscript 0 L subscript f equals I subscript omega equals open square brackets fraction numerator m l squared over denominator 12 end fraction plus open parentheses fraction numerator m l squared over denominator 12 end fraction plus m l squared close parentheses close square brackets omega equals 7 over 6 m l squared omega L subscript i equals L subscript f text or end text omega equals omega subscript 0 over 7$

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