Question

A Centigrade and Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers a temperature of $140^{\circ }$. The fall of temperature as registered by the Centigrade thermometer is :

• A. $80^{\circ }C$
• B. $40^{\circ }C$
• C. $50^{\circ }C$
• D. $90^{\circ }C$

Answer 1

Answer: (B)

Fall in temperature in Centigrade thermometer = Initial temperature of boiling water - fall in temperature.
The relation between Centigrade ${}^{\circ }C$ scale of temperature and Fahrenheit ${}^{\circ }F$ scale is
$\frac{C}{5}=\frac{F-32}{9}$.
Given, Fahrenheit $F=140^{\circ }F$
$\therefore \frac{C}{5}=\frac{140-32}{9}=\frac{108}{9}=12$
$\Rightarrow C=12\times 5=60^{\circ }C$
$\therefore$ Fall in temperature in centigrade scale
$=$ initial temperature $-$ full in temperature
$=100^{\circ }C-60^{\circ }C=40^{\circ }C$