Answer
Verified
40.8k+ views
Hint: Temperature is the degree of hotness or coldness of the body. It is measured using a device called a thermometer and has the dimensions of the Kelvin, Celsius, Fahrenheit etc. Out of which the Kelvin is the base unit of the temperature and the Celsius is the base unit of temperature.
Formula used:
The relation between the Celsius and the Fahrenheit is
$F = \dfrac{9}{5}C + 32$
Where $F$ is the temperature in Fahrenheit and $C$ is the temperature in the scale of Celsius.
Complete step by step solution:
In the scale of the Celsius, the zero degree represents the freezing point of the water and the $100$ degree represents the boiling point of the water. Let us consider the basic formula between the Celsius and the Fahrenheit which is given above.
$F = \dfrac{9}{5}C + 32$
Rearranging the above formula based on the given options,
$\left( {F - 32} \right)5 = 9C$
Forming the denominators from the above equation,
$\Rightarrow$ $\dfrac{{F - 32}}{9} = \dfrac{C}{5}$
By interchanging the left and right hand side of the equation.
$\Rightarrow$ $\dfrac{C}{5} = \dfrac{{F - 32}}{9}$
By dividing both the sides by $20$ ,
$\Rightarrow$ $\dfrac{C}{{5 \times 20}} = \dfrac{{F - 32}}{{9 \times 20}}$
By performing the basic arithmetic operation,
$\Rightarrow$ $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$
Hence among the given option for the relation between the Celsius and the Fahrenheit scales, $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$ is the correct answer.
Thus the option (B) is correct.
Note: The Fahrenheit scale is used for the measurement of the body temperature, and it is used in the weather forecasting in the United states and other countries. Even though there emerged many temperature naming units, the Americans still use Fahrenheit for their easy dimensioning.
Formula used:
The relation between the Celsius and the Fahrenheit is
$F = \dfrac{9}{5}C + 32$
Where $F$ is the temperature in Fahrenheit and $C$ is the temperature in the scale of Celsius.
Complete step by step solution:
In the scale of the Celsius, the zero degree represents the freezing point of the water and the $100$ degree represents the boiling point of the water. Let us consider the basic formula between the Celsius and the Fahrenheit which is given above.
$F = \dfrac{9}{5}C + 32$
Rearranging the above formula based on the given options,
$\left( {F - 32} \right)5 = 9C$
Forming the denominators from the above equation,
$\Rightarrow$ $\dfrac{{F - 32}}{9} = \dfrac{C}{5}$
By interchanging the left and right hand side of the equation.
$\Rightarrow$ $\dfrac{C}{5} = \dfrac{{F - 32}}{9}$
By dividing both the sides by $20$ ,
$\Rightarrow$ $\dfrac{C}{{5 \times 20}} = \dfrac{{F - 32}}{{9 \times 20}}$
By performing the basic arithmetic operation,
$\Rightarrow$ $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$
Hence among the given option for the relation between the Celsius and the Fahrenheit scales, $\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$ is the correct answer.
Thus the option (B) is correct.
Note: The Fahrenheit scale is used for the measurement of the body temperature, and it is used in the weather forecasting in the United states and other countries. Even though there emerged many temperature naming units, the Americans still use Fahrenheit for their easy dimensioning.
Recently Updated Pages
silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main
A parallel plate capacitor has a capacitance C When class 12 physics JEE_Main
A series combination of n1 capacitors each of value class 12 physics JEE_Main
When propyne is treated with aqueous H2SO4 in presence class 12 chemistry JEE_Main
Which of the following is not true in the case of motion class 12 physics JEE_Main
The length of a potentiometer wire is 10m The distance class 12 physics JEE_MAIN
Other Pages
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
Amongst LiCl RbCl BeCl2 and MgCl2the compounds with class 11 chemistry JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main
In an electromagnetic wave A Power is equally transferred class 12 physics JEE_Main
Write dimension of force density velocity work pre class 11 physics JEE_Main
A food packet is dropped from a helicopter rising up class 11 physics JEE_Main