A rod of length `l` whose lower end is fixed on a horizontal plane, starts toppling from the vertical position. The velocity of the upper end when it hits the ground is.

Options

A. `sqrt(g //l)`
B. `sqrt(3 g l)`
C. `3 sqrt(g//l)`
D. `sqrt(3 g//(l)`

Answer

B

Explanation

(b) loss in `PE` = gain in `KE`
`mg (l)/(2) =(1)/(2) I_A omega^2 rArr mg l/(2) = (1)/(2) (ml^2)/(3) omega^2 rArr omega = sqrt((3g)/(l))`
`v = omega l = (sqrt(3 g//l)) l = sqrt(3 gl)`.