Correct option: (C) √(6gL)
Explanation:
In one full revolution the increase in P.E = MgL, (L = length of rod, M = is the mass of rod)
By conservation of energy,
MgL = (1/2)Iω2
for rod, I = (ML2 / 3)
hence
MgL = (1/2) × (ML2 / 3) × ω2
g = (1/6)Lω2
ω2 = (6g / L)
Velocity = V = r × ω
here r = L
hence
V = Lω
= L × √(6g / L)
= √(6gL)