A uniform L-shaped rod of mass 2m and length 2L, hangs from a hinge as shown (AO is horizontal and OB is vertical). If it is released from the position shown, then find the maximum angular velocity acquired by the end.
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Options

A. `sqrt((3g)/l)`
B. `sqrt((3g)/l (sqrt(2)-1))`
C. `sqrt((3g)/(2l)(sqrt(2)-1))`
D. `sqrt((3g)/(2l) (sqrt(2)+1))`

Answer

3

Explanation

`omega_(max)` is when em is at lowest position

`y_(0)=(ml//2)/(2m)=l/4`
`y=l/(2sqrt(2))`
`omega_(g)=2mg(l/(2sqrt(2))-l/4)=1/2 ((ml^(2))/3xx2) omega^(2)`
`rArr w=sqrt((3g)/(2l)(sqrt(2)-1))`