Dimension of Tension and its Derivation | Tension Dimensional Formula

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Dimension of Tension: Tension is a pulling force that acts along a medium that is being applied an external force. This tension acts axially i.e. along with length. The action-reaction pair of forces that are present at each end of the element can also be referred to as tension. The opposite of compression might be tension. Tension Dimensional Formula is

M1L1T -2

In this article, we obtain the Dimension of Tension along with its derivations.

Dimension of Tension

Dimension of Tension and Its Derivation

Since Surface Tension is a type of Force, the Dimension of Tension is equal to the Dimension of Force

~=~{M^1L^1T^{-2}}

Also read:

Dimension of Speed of LightDimension of Surface Tension

Derivation of Dimension of Tension

The Dimensional Formula is written as follows.

~=~{M^{a}L^{b}T^{~c}}

Where,

M represents Mass

L represents Length

T represents Time

and a, b and c are the powers of M, L and T respectively

Dimension of Mass = M1L0T0

Dimension of Distance = M0L1T0

Dimension of Time = M0L0T1

Dimension of Velocity = M0L1T-1 (obtained by dividing Dimension of Distance by Dimension of Time)

Since we know that 

Acceleration~=~{Change~In~Velocity}/{Time~Period}

Hence

Dimension~of~Acceleration~=~{Dimension~of~Velocity}/{Dimension~of~Time}

~=~{M^0L^1T^{-1}}/{M^0L^0T^{1}}

~=~{M^0L^1T^{-2}}

Also, we know that

Force~=~Mass~*~Acceleration

F~=~m~*~a

Dimensiom~of~Force~=~Dimensiom~of~Mass~*~Dimensiom~of~Acceleration

~=~{M^1L^0T^{0}}~*~{M^0L^1T^{-2}}

~=~{M^1L^1T^{-2}}

Hence, proved that the Dimension of Tension is M1L1T-2

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