The periodic time of a simple pendulum, (the simple pendulum with its bob is in air) is T. But if the bob of the simple pendulum is completely immersed in a non viscous liquid, whose density is 20 1

Question

The periodic time of a simple pendulum, (the simple pendulum with its bob is in air) is T. But if the bob of the simple pendulum is completely immersed in a non viscous liquid, whose density is 20 1 ​ times the density of material of the bob, then its new period will be

TestHub · Accepted Answer

The time period of a simple pendulum in air is given by $T = 2 π \frac{L}{g}$ .

When the bob is immersed in a liquid, the effective acceleration due to gravity $g^{'}$ becomes:

$g^{'} = g (1 - \frac{ρ}{σ})$

where $ρ$ is the density of the liquid and $σ$ is the density of the material of the bob.

Given that $ρ = \frac{σ}{20}$ , we have:

$g^{'} = g (1 - \frac{1}{20}) = \frac{19 g}{20}$

The new time period $T^{'}$ is:

$T^{'} = 2 π \frac{L}{g ^{'}} = 2 π \frac{L}{\frac{19 g}{20}} = 2 π \frac{L}{g} \frac{20}{19}$

$T^{'} = \frac{20}{19} T$

Answer: $\frac{20}{19} T$

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