Question

Define Absolute and gravitational units of force. What are dimensions of force ?

Answer 1

Hint: The absolute unit of a physical quantity is the SI unit at which it is measured. The gravitational unit is only applicable for force. The gravitational unit of force is the unit in which the force exerted is calculated.

Formulae used:
$F = ma$ where $F$ is the force to be calculated, $m$ is the mass of the involved body/ bodies and $a$ is the acceleration provided to the body/ bodies of mass $m$

Complete step by step solution:
Newton, absolute unit of force within the Systeme International d'Unites of Units (SI units), is abbreviated as N. It is defined as the force necessary to supply a mass of 1 kilogram with an acceleration of 1 metre per second per second. One newton is equivalent to a force of 100,000 dynes in the centimetre-gram-second (CGS) system, or a force of about 0.2248 pound in the foot-pound-second (English, or customary) system. The unit Newton was named after Sir Isaac Newton, who introduced classical physics and gave us the three laws of motion which describes the various changes that a force can produce in the motion of a body.
The kilogram force (\[kgf\]) is the gravitational unit of force. The force exerted by the earth on a body of mass $1kg$ is regarded as \[1{\text{ }}kgf\].
$F = ma$
$1kgf = 1kg \times 9.8m/s$
$1kgf = 9.8\dfrac{{kg \times m}}{{{s^2}}} = 9.8N$___________________(i)

Now, for finding the dimensions of force, from equation (i), we get
$
   \Rightarrow 9.8N = 9.8\dfrac{{kg \times m}}{{{s^2}}} \\
   \Rightarrow N = \dfrac{{kg \times m}}{{{s^2}}} \\
$
Using dimensional analysis, we can rewrite the above equation as
$
   \Rightarrow N = \dfrac{{kg \times m}}{{{s^2}}} \\
   \Rightarrow N = \dfrac{{\left[ {ML} \right]}}{{\left[ {{T^2}} \right]}} \\
   \Rightarrow N = \left[ {ML{T^{ - 2}}} \right] \\
$
Therefore, this is the dimension of force.

Note: Gravitational unit of force is not only valid for earth, but for other planets too. The acceleration due to gravity varies from planet to planet. Hence the value of kgf changes from one planet to another.