A uniform rod of legth `L` is free to rotate in a vertica plane about a fixed horizontal axis through `B`. The rod begins rotating from rest. The angular velocity `omega` at angle `theta` is given as

Options

A. `sqrt(((6g)/(L)))sin((theta)/(2))`
B. `sqrt(((6g)/(L)))cos((theta)/(2))`
C. `sqrt(((6g)/(L)))sintheta`
D. `sqrt(((6g)/(L)))costheta`

Explanation

Decrease in gravitational kinetic energy
`=` increase in rotational kinetic energy
`therefore((l)/(2)-(l)/(2)costheta)=(1)/(2)Iomega^(2)`
`=(1)/(2)((ml^(2))/(3))omega^(2)`
`omega=sqrt((6g)/(L))sin((theta)/(2))`