Question

A rod of length `L`, hinged at the bottom is held vertically and then allowed to fall, the linear velocity of its top when it hits the floor is
A. `sqrt(2gL)`
B. `sqrt((2g)/(L))`
C. `sqrt(3gL)`
D. `sqrt((3g)/(L))`

Answer 1

By the energy conservation
`mg((L)/(2))=(1)/(2)I_(0)omega^(2)=(1)/(2)xx(mL^(2))/(3)omega^(2)`
`omega=sqrt((3g)/(L))`
`v=omegaL=sqrt3gL`