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Question: The CGS unit of pressure is ______ A. \(dyne\text{ }c{{m}^{-2}}\) B. \(N\text{ }{{\text{m}}^{-2...

The CGS unit of pressure is ______
A. dyne cm−2dyne\text{ }c{{m}^{-2}}
B. N m−2N\text{ }{{\text{m}}^{-2}}
C. J m−2J\text{ }{{\text{m}}^{-2}}
D. dyne cm−3dyne\text{ }c{{m}^{-3}}

Explanation

Solution

Pressure is defined as the ratio of the force applied to the surface area. Using this formula obtains the units of the pressure by putting the units of the individual terms involved in the formula in the same relation of the terms. Also try to understand what system of units are CGS and try to convert the obtained units into CGS units.

Complete answer:
We need to find the CGS unit of pressure
Pressure can be defined as the ratio of the force applied to the surface area, mathematically this is represented as P=FAP=\frac{F}{A}
We know that the force is the product of mass and acceleration whose units are kgkg and ms−2m{{s}^{-2}}
And hence the units of force is obtained as kg⋅m⋅s−2kg\cdot m\cdot {{s}^{-2}} this is also called as Newton represented as N and the units of area is m2{{m}^{2}}
Put these units in the place of their respective terms, we obtain the units of the pressure is kg⋅m−1⋅s−2kg\cdot {{m}^{-1}}\cdot {{s}^{-2}}or Nm2\frac{N}{{{m}^{2}}}
The units we obtained are in MKS system also called as SI system
The CGS system of Newton and meter are dynedyne and centimeter
Hence the CGS unit of pressure is dyne cm−2dyne\text{ }c{{m}^{-2}}

So the option (A) is the correct answer.

Note:
The expansion of the MKS system is Meter Kilogram Second, this system is also called as SI system of units, these are the standard units which are followed internationally and the expansion of CGS system is Centimeter Gram Second.