Question

Two new thermometer scales X and Y are plotted as shown. The LFP and UFP of Y-scale are ${{0}^{0}},{{90}^{0}}$ respectively. Then the corresponding values on X-scale are

$\begin{align}
  & a)-{{10}^{0}},{{100}^{0}} \\
 & b){{0}^{0}},{{80}^{0}} \\
 & c){{10}^{0}},{{90}^{0}} \\
 & d){{10}^{0}},{{100}^{0}} \\
\end{align}$

Answer 1

Hint: The graph given is in terms of the two thermometer scales x and y. If we find the graph equation, we can find a relation between the two thermometers x and y. As the lower and upper freezing points of the first thermometers are given, we can find the upper and lower freezing points of the second one using the relation between them.

Complete step by step answer:
Let us first write down the five terms,
LFP of the thermometer Y is ${{0}^{0}}$
UFP of the thermometer Y is ${{100}^{0}}$
Let us find the graph equation now,
It is a straight line, so the equation will be of form y=mx+c.
The slope of the line is equal to
$\begin{align}
  & m=\tan {{45}^{0}} \\
 & m=1 \\
\end{align}$
The constant is the y coordinate when x is equal to 0.
Therefore, c=-10.
Now, the equation we get is,
$y=x-10$
Let us find the LFP of the thermometer X as Value of Y is given.,
$\begin{align}
  & y=mx+c \\
 & \Rightarrow 0=x-10 \\
 & \Rightarrow x={{10}^{0}} \\
\end{align}$
Therefore, the LFP of the thermometer X is 10 degrees.
Now, the UFP of the thermometer X can be founds similarly as,
$\begin{align}
  & y=x-10 \\
 & \Rightarrow 90=x-10 \\
 & \Rightarrow x={{100}^{0}} \\
\end{align}$
Hence, the UFP of the thermometer X is 100 degrees.

So, the correct answer is “Option D”.

Additional Information:
A thermometer is a device used to measure the temperature or the temperature gradient. A temperature gradient is the degree of hotness or coldness of a body. Thermometer will have two important components, one is a temperature sensor, where some change occurs when there’s change in temperature and the other is the conversion of the change into numerical value. In a thermometer, bulb of a mercury-in-glass thermometer or the pyrometric sensor in an infrared thermometer. The visible scale that is marked on a mercury-in-glass thermometer.

Note:
The slope of the above equation in the above question is found by finding the tangent of the angle made by the line with the x-axis. Also, the constant is taken as -10 because the y- coordinate is equal to -10 when x is equal to zero. If the y=0 when x=0, then constant value will be equal to zero.