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PhysicsFluidBernoulli's theorem and applicationsMedium2 minQB

PhysicsMediuminteger

A vertical cylindrical vessel is filled with water and made to rotate about its axis with a time period of $T_{0}$ . Due to cool air a thin layer of ice is formed at the free surface. A small disc is released on the solidified free surface close to the axis. The time period of the small oscillations of the disc is $x T_{0}$ . Find $x$ .

Answer:

Solution:

The free surface of the water is $y = \frac{ω ^{2} x ^{2}}{2 g}$ . The energy expression for the sliding disc is

$\frac{1}{2} mv^{2} + mg y = E \frac{mv ^{2}}{2} + mg \frac{ω ^{2} x ^{2}}{2 g} = E \Rightarrow \frac{d ^{2} y}{dt ^{2}} + ω^{2} x = 0 \Rightarrow T = T_{0}$

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Bernoulli's theorem and applications

⏱ 2mℹ️ Source: QB

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