Assertion: On moon barometer height will be six times compared to the height of earth.
Reason: Value of g on the moon's surface is $\dfrac{1}{10}$ the value of g on earth’s surface.
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.

Hint: In the given assertion reason type question we need to check if the assertion statement is right or wrong. We know that a barometer is a device which is used to measure atmospheric instruments. To know if the statement is right or wrong we need to know the relation between atmospheric pressure on earth and moon. Next we need to consider the reason. We know the value of ‘g’ on earth and ‘moon’. Using the relation between ‘g’ on earth and moon we will know if the given reason is right or wrong. Thus we will get the solution.

Complete step by step answer:
In the question the assertion is given as on the surface of the moon the height of the barometer will be six times the height of the barometer on earth’s surface.
Let us see if this statement is right or wrong.
We know that the moon does not have an atmosphere and hence the atmosphere pressure of the moon is zero.
Hence the height of the barometer will also be zero. Thus the height of the barometer on the surface of the moon will be less than the height of the barometer on the earth’s surface.
Therefore this statement is wrong.
Now in the reason it is given that the value of g on the moon’s surface is ${{\dfrac{1}{10}}^{th}}$ times the value of g on earth’s surface.
We know that the value of acceleration due to gravity on the moon is approximately $1.625m/{{s}^{2}}$ and we also know that acceleration due to gravity on earth’s surface is $9.8m/{{s}^{2}}$.
By comparing these two values, we can see that the value of acceleration due to gravity on the surface of the moon is $\dfrac{1}{6}$ times the value of acceleration due to gravity on the surface of earth.
Thus we can see that the reason is also wrong.
Therefore we can say that both assertion and reason are incorrect.

So, the correct answer is “Option D”.

Note:
In an assertion reason type question, one statement will be given as assertion and another statement reason. First we need to check if the assertion statement is correct and later we will check if the reason is correct. If both assertion and reason are correct then we need to check if reason is the correct explanation for assertion. Thus we will get the solution.