Question 285: Oscillations

Question

A simple pendulum has a time period '$$T$$' in air. Its time period when it is completely immersed in a liquid of density one eighth the density of the material of bob is

Accepted Answer

Time period of simple pendulum $$\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$$
$$\Rightarrow \mathrm{T} \propto \frac{1}{\sqrt{\mathrm{g}}}$$
Net downward force acting on the bob inside the liquid $$=$$ Weight of bob $$-$$ Upthrust
$$\Rightarrow \mathrm{Vpg}-\mathrm{V} \frac{ho}{ho} \mathrm{g}=\frac{7}{8} \mathrm{~V} ho \mathrm{g}$$
The value of $$g$$ inside the liquid will be $$\frac{g}{8}$$
$$	herefore \quad$$ Time period in liquid $$\mathrm{T}_1=\frac{1}{2 \pi} \sqrt{\frac{\frac{l}{7}}{8}} =\sqrt{\frac{8}{7}} \mathrm{~T}$$

Answer

$$\left(\sqrt{\frac{7}{8}}\right) \mathrm{T}$$

Answer

$$\left(\sqrt{\frac{5}{8}}\right) \mathrm{T}$$

Answer

$$\left(\sqrt{\frac{3}{8}}\right) \mathrm{T}$$

Answer

$$\left(\sqrt{\frac{8}{7}}\right) \mathrm{T}$$

Oscillations

A simple pendulum has a time period '$T$' in air. Its time period when it is completely immersed in a liquid of density one eighth the density of the material of bob is

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