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A thermometer graduated according to a linear scale reads a value x₀ when in contact with boiling water, and $\frac{x_{0}}{3}$ when in contact with ice. What is the temperature of an object in ^oC , if this thermometer in the contact with the object reads $\frac{x_{0}}{2}$ ?
Option 1)
25
Option 2)
60
Option 3)
35
Option 4)
40

Answers (1)

best_answer

For Uniform Temperature -

$\frac{\theta_{1}-\theta_{2}}{l}=\frac{\Delta \theta}{\Delta x}$

- wherein

Unit - K/m or ^oC/m

Dimension $L^{-1}\theta$

$\frac{x_{0}}{3}$ is equivalent to $0^{\circ}c$

& $x_{0}$ is equivalent to $100^{\circ}c$

So we get

$\frac{x-\frac{x_{0}}{3}}{x_{0}-\frac{x_{0}}{3}}=\frac{T-0}{100-0}$

put $x=\frac{x_{0}}{2}$

so $\frac{\frac{x_{0}}{2}-\frac{x_{0}}{3}}{\frac{2x_{0}}{3}}=\frac{T}{100}$

$\Rightarrow \frac{x_{0}}{6\times \frac{2x_{0}}{3}}=\frac{T}{100}$

$T=\frac{100}{4}=25^{\circ}C$

so , $T=25^{\circ}C$

Option 1)
25
Option 2)

60

Option 3)

35

Option 4)

40

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