A uniform rod of mass m and length L is hinged about one end and can freely rotate in a vertical plane. The angular velocity of the rod, when it falls from position P to Q. through an angle `alpha` starting from rest, is

Options

A. `sqrt((6g)/(5L)) sin alpha`
B. `sqrt((6g)/(L)) sin alpha/2`
C. `sqrt((6g)/L) cos alpha/2`
D. `sqrt((6g)/L) sin alpha`

Answer

B

Explanation

Loss in GPE = gain in KE
`rArr mg l/2 (1- cos alpha) =1/2(ml^(2))/3 omega^(2) rArr omega = sqrt((3g)/l (1- cos alpha))=sqrt((6g)/t) sin alpha/2`