Question 160: Properties of Matter

Question

A simple pendulum oscillating in air has period
T. The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is
1/16 th of the material of the bob.
If the bob is inside liquid all the time, its period
of oscillation in this liquid is :

Accepted Answer

For a simple pendulum T = $$2\pi \sqrt {{L \over {{g_{err}}}}} $$
Situation 1: when pendulum is in air $$ 	o $$ g
eff
= g
Situation 2:when pendulum is in liquid
$$ 	o $$ g
eff
= $$\left( {1 - {{{ho _{liquid}}} \over {{ho _{body}}}}} ight) = g\left( {1 - {1 \over {16}}} ight) = {{15g} \over {16}}$$
So, $${{{T^{'}}} \over T} = {{2\pi \sqrt {{L \over {15g/16}}} } \over {2\pi \sqrt {{L \over g}} }}$$
$$ \Rightarrow {T^{'}} = {{4T} \over {\sqrt {15} }}$$

Answer

$$2T\sqrt {{1 \over {10}}} $$

Answer

$$4T\sqrt {{1 \over {14}}} $$

Answer

$$4T\sqrt {{1 \over {15}}} $$

Answer

$$2T\sqrt {{1 \over {14}}} $$

Properties of Matter

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :

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