A simple pendulum oscillates in simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is 4/3×1000kg/m3.  Which of the given relationship between t and t0 is true?

The time period of simple pendulum in airT=t0=2πlg… (i)l, being the length of simple pendulum. In water, effective weight of bobw′=weight of bob in air - upthrust⇒ ρVgeff =mg−m/g=ρVg−ρ′Vg=ρ−ρ′Vgwhere ρ′= density of bob.ρ=density of water∴ geff=ρ−ρ′ρg=1−ρ′ρg∴   t=2πl1−ρ′ρg⋯Thus,    tt0=11−ρ′ρ=11−1000(4/3×1000)=44−3=2⇒ t=2t0