Question

The dimensions of pressure gradient are:
A. $\left[ {M{L^{ - 2}}{T^{ - 2}}} \right]$
B. $\left[ {M{L^{ - 2}}{T^{ - 1}}} \right]$
C. $\left[ {M{L^{ - 1}}{T^{ - 1}}} \right]$
D. $\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$

Answer 1

Hint: First let us see what is meant by pressure gradient:
In atmospheric science, the pressure gradient (regularly of air however more by and large of any liquid) is a physical amount that portrays in which course and at what rate the pressure expands the most quickly around a specific area.

Complete step by step answer:
Since wind is created by differences in air pressure, it is imperative to comprehend pressure inclinations, which are the round lines around a high or low weight framework. Air pressure is made by the movement, size, and number of gas particles present noticeable all around. This fluctuates dependent on the temperature and thickness of the air mass.

Inside the air, there are a few powers that sway the speed and heading of winds. The most significant however is the Earth's gravitational power. As gravity packs the Earth's climate, it makes air pressure the main force of wind. Without gravity, there would be no climate or air pressure and accordingly, no wind.
The force actually responsible for causing the movement of air though is the pressure gradient force.

Contrasts in air pressure and the pressure gradient force are brought about by the inconsistent warming of the Earth's surface when approaching sunlight based radiation accumulates at the equator. Warm air is less thick and has a lower barometric pressure than the cold air at a much greater height.
To show wind speeds on a climate map, the pressure gradient is plotted utilizing isobars planned between regions of high and low weight. Bars divided far separated shows gradual pressure gradient and light winds.
Lines that are nearer together show a steep pressure gradient and strong winds.
The pressure gradient is mathematically given by:
$P = \dfrac{{{\text{Change}}\,{\text{in}}\,{\text{pressure}}}}
{{{\text{change}}\,{\text{in}}\,\,{\text{distance}}}}$

So, the dimensional formula is given by:
$
  P = \dfrac{{M{L^{ - 1}}{T^{ - 2}}}}{L} \\
   = \left[ {M{L^{ - 2}}{T^{ - 2}}} \right] \\
$

So, the correct answer is “Option A”.

Note:
So, in short we can say that a pressure gradient is the pace of progress (inclination) of climatic (barometric) pressure concerning horizontal distance at a given point in time.
Also arm air is less thick and has a lower barometric pressure than the cold air at a much greater height.