A bob of mass m on a thread of length l oscillates with time period T. The bob is then immersed in a liquid whose density is 1/4 of the density of the bob, and the thread is lengthened by 1/3 of its original length. The new time period of the small oscillations is

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(2) 4/3 T. Buoyancy reduces the effective gravity to g'=g(1-σ/ρ)=g(1-1/4)=(3g)/4. The new length is l'=l+l/3=(4l)/3. T'=2π√(4l/3)/(3g/4)=2π√(16l)/(9g)=4/3 T.

A bob of mass m on a thread of length l oscillates with time period T. The bob is then immersed in a liquid whose density is 1/4 of the density of the bob, and the thread is lengthened by 1/3 of its original length. The new time period of the small oscillations is

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