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Q.

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

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a

10 °, 100 °

b

0 °, 80 °

c

10 °, 90 °

d

10 °, 100 °

answer is D.

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Detailed Solution

Concept: 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.
Let us first write down the five terms,
LFP of the thermometer Y is

0 °

UFP of the thermometer Y is

100 °

Let us find the graph equation now,
It is a straight line, so the equation will be of the form y=mx+c.
The slope of the line is equal to

m = \tan 45 °

m = 1

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.,

y = mx + c \Rightarrow 0 = x - 10 \Rightarrow x = 10 °

Therefore, the LFP of the thermometer X is 10 degrees.
Now, the UFP of the thermometer X can be found similarly as,

y = x - 10 \Rightarrow 90 = x - 10 \Rightarrow x = 100 °

Hence, the UFP of the thermometer X is 100 degrees.
Hence, option 4 is correct.

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