A cylindrical block of wood (density = 650 kg/m³), of base area 30 cm² and height 54 cm, floats in a liquid of density 900 kg/m³. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) 52 cm, 26 cm, 39 cm, 65 cm

As block is floating it's weight should be equal to buoyancy force
ρwoodVcylinderg = ρliquidVdisplacedg
Vdisplaced = (ρwood/ρliquid)Vcylinder .. (i)
After displacing by small distance x, the net force on cylinder will be
F = Buoyancy - w = ρliquid(Vdisplaced + AcylinderΔx)g - ρwoodVcylinderg
F = ρliquidVdisplacedg + ρliquidAcylinderΔxg - ρwoodVwoodg
the net force on cylinder becomes
from equation (i) ρwoodVcylinderg = ρliquidVdisplacedg
F = ρliquidAcylinderΔxg
m a = ρliquidAcylinderΔx g
a = (ρliquidAcylinder/m)Δx
a = ω²Δx
ω² = ρliquidAcylinder/ρcylinderVcylinder
ω² = ρliquidAcylinder/(ρwoodAcylinderhcylinder)
ω² = (ρliquid/ρwood)hcylinder
ω² = (900/650) × 54
This should be equal to angular frequency of simple pendulum
ω = √(g/l)
√(900/650 × 54) = √(g/l)
l = g(650 × 54)/900
l = 0.39 × 65 = 39 cm