Question

The expression has the same SI base units as pressure?
(A) $ \dfrac{{force}}{{length \times speed}} $
(B) $ \dfrac{{force}}{{length \times time}} $
(C) $ \dfrac{{mass}}{{length \times {{(time)}^2}}} $
(D) $ \dfrac{{mass \times {{(time)}^2}}}{{length}} $

Answer 1

Hint :Pressure is the force applied which is perpendicular to the surface of objects and is taken per unit area or it can be said as the amount of force exerted per area. In order to find the answer to the above question we have to simplify the equation of pressure.

Complete Step By Step Answer:
As pressure is given by force per unit area, the expression will be,
 $ Pressure = \dfrac{{Force}}{{Area}} $
As asked in questions, we have to convert the quantities into their SI unit, so the equation will become
 $ Pressure = \dfrac{{Newton}}{{Area}} $
As there is no option as per the obtained equation, so we have to further break it down to its base units, So, the equation will become,
 $ Pressure = \dfrac{{mass \times acceleration}}{{Area}} $
Putting $ acceleration = \dfrac{{length}}{{{{(time)}^2}}} $ in the above equation, we will get,
 $ Pressure = \dfrac{{mass \times length}}{{Area \times {{(time)}^2}}} $
As area can be written as square of length, so the above equation will become,
 $ Pressure = \dfrac{{mass}}{{length \times {{(time)}^2}}} $
Hence the correct option is C.

Additional Information:
There are basically two types of pressure, absolute pressure and gauge pressure which is distinguished by what is taken as reference to compare them, which is called the reference pressure.

Note :
The SI unit of the pressure is Pascal. It is denoted by Pa. Here in this question one has to find the answer according to the given options, as we also saw that there can be multiple ways or units to denote pressure, also force is not a unit but a quantity.