A uniform rod of mass M & length L is hinged about its one end as shown. Initially it is held vartical and then allowed to rotate, the angular velocity of rod when it makes an angle of `37^(@)` with the vertical is

Options

A. `((g)/(L))^(1//2)`
B. `((3g)/(4L))^(1//2)`
C. `((3 sqrt3g)/(2l))^(1//2)`
D. `((3g)/(2l))^(1//2)`

Answer

D

Explanation

`cos 60^(@)= ((L)/(2)- Delta h)/(L//2)`
`rArr (L)/(2)- Delta h= (L)/(4)`
`rArr Delta h= (L)/(4)`

Decreases is PE= `Mg Delta h= "Mg" (L)/(4)`
K.E. of rotation `=(1)/(2) I omega^(2)= (1)/(2) .(ML^(2))/(3) omega^(2)`
`rArr "Mg" (L)/(4) = (ML^(2))/(6) omega^(2)`
`rArr omega^(2) = (6g)/(4L) rArr omega= sqrt((3g)/(2L))`