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A thin string is held at one end and osc...

A thin string is held at one end and oscillates so that,
`y(x = 0, t) = 8 sin 4t(cm)`
Neglect the gravitattional force. The string's linear mass density is `0 .2 kg// m` and its tension is ` 1 N`. The string passes through a bath filled with `1 kg` water. Due to friction heat is transferred to the bath. The heat transfer efficiency is `50%`. Calculate how much time passes before the temperature of the bath rises one degree kelvin?

Text Solution

Verified by Experts

`v=sqrt((T)/(mu))=sqrt((1)/(0.2))=2.236m//s`
further `rhoS=mu=0.2 kg//m`
Te average power over a period is `P=(1)/(2)(rhoS) omega^(2)A^(2)v`
Substituting the values, we have `P=2.29xx10^(-2)J//s`
Now let, it takes t second to raise the temperature of 1 kg water by one degree kelvin. Then `Pt=ms Deltat`
Here S= specific heat of water `=4.2xx10^(3)J//kg-K`
`:.t=(msDeltat)/(P)=((1)(4.2xx10^(3))(1))/(1.145xx10^(-2))~~4.2` day
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