#"it will gain a potential energy if object is brought at horizontal position."#

#E_p=m*g*h#

#m:"mass of object"#

#g:"acceleration of gravity"#

#h=l/2#

#E_p=m*g*l/2#

#"it will turn and will gain a kinetic energy if object is released"#

#E_k=1/2*I*omega^2#

#I " represents the moment of inertia of rod"#

#omega" represents angular velocity of object"#

#"we can write "E_p=E_k " because Energy is reserved."#

#m*g*l/cancel(2)=1/cancel(2)*I*omega^2#

#m*g*l=I*omega^2#

#" so " I=1/3*m*l^2" (moment of inertia for a rod turning its one end)"#

#"we can write as:"#

#cancel(m)*g*cancel(l)=1/3*cancel(m)*cancel(l^2)*omega^2#

#g=1/3l*omega^2#

#omega^2=(3g)/l#

#sqrt(omega^2)=sqrt((3g)/l)#

#omega=sqrt((3g)/l)#