A thin bar of mass `M` and length `L` is free to rotate about a fixed horizontal axis through a point at its end. The bar is brought to a horizontal position and then released. The axis is perpendicular to the rod. The angular velocity when it reaches the lowest point is

Options

A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
C. dependent only upon the acceleration due to gravity and the length of the bar
D. directly proportional to its length and inversely proportional to the acceleration due to gravity

Answer

B, C, D

Explanation

Gain in `KE =`Loss in `PE`
`implies 1/2Iomega^(2)=mgl/2implies1/2 (ml^(2))/3omega^(2)=mgl/2`
`implies omega=sqrt((3g)/l)`