Dimensions of Tension

Dimensional Formula of Tension is [MLT^-2]

Tension is a force experienced by objects such as rope or string when a mass is attached to it. It is given as the sum of the forces experienced by the string. Tension forces act in pairs of action and reaction. In this article, we will learn what is Dimensional Formula of Tension is, along with its derivation with a brief introduction to its definition.

Tension Definition

Tension is a force that acts along a medium’s length, such as a rope or thread. A force is needed to place these items under stress. An exciting pair, like an action-reaction pair, is another name for tension. The tension force is accessible at every point along the string. Hence, Tension is a force with a new and better name, it is nothing at all.

Tension Formula

Tension experienced by an Object can be calculated by the tension formula on a body by multiplying the mass by acceleration and the product of mass and gravitational force.

T = mg + ma = (g + a)

Learn, Tension Formula

What is Dimensional Formula of Tension?

Tension is Dimensionally Represented as [M¹ L¹ T ^-2]

where,

• M represents Mass
• L represents Length
• T represents Time

Derivation of Dimensional Formula of Tension

Tension is given as sum of two forces. Hence, Tension in physical terms is actually a force. The dimensions of tension equal the dimensions of force.

Formula of Force is,

F = M × a

Dimensions of Force is given by muiltiplying dimension of mass and aceleration

• Dimension of Mass = [M¹ L⁰ T⁰]
• Dimesnion of Acceleration = [M⁰ L¹ T^-2]

When we substitute value of mass and acceleration into equation, we get

Force = M × a

Dimesion of Tension = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-2] = M¹ L¹ T^-2

Hence, M¹ L¹ T^-2 is the dimensional representation of tension.

Advantages and Disadvantages of Dimensional Formula

The advantages and disadvantages of Dimensional Formula are mentioned below:

Advantages of Dimensional Formula

• used to verify that the provided equation is accurate. The homogeneity concept is the foundation of this utilization.
• Use to change the units of measurement from one system to another.
• Utilize to obtain the formulas illustrating the relationships between various physical quantities.
• Used to find the dimensions of physical quantities that are either constant or unknown
• There are fewer experiments carried out.

Disadvantages of Dimensional Formula

• This approach cannot determine dimensionless quantities. Using this method, the constant of proportionality cannot be found.
• Logarithmic, exponential, and trigonometric functions cannot be used with this approach.
• This method cannot be applied if one side of the equation involves the addition or subtraction of physical quantities.
• Dimensional analysis is not able to validate the validity of a physical quantity connection.
• For the correlation of more than three parameters, it is not feasible.
• The nature of the unidentified physical quantities cannot be ascertained by dimensional analysis.
• There’s a chance that results from several studies won’t match up.

Read More,

• Dimensional Formula
• Stress and Strain
• Young’s Modulus

Dimensional Formula of Tension – FAQs

1. What is Tension?

Tension is a force along the length of a medium, especially a force carried by a flexible medium, such as a rope or cable.

2. What is the Unit of Tension?

The unit of Tension is Newton

3. How to derive Dimension of Tension?

Tension is a type of force and the Formula F = M × a provides the dimensions of force, from which the dimension of tension is obtained.

4. Is Dimension of Tension and Force same?

Yes, the dimesnion of Tension and Force are same.

5. Is Tension and Stress Same?

No, Tension and stress are not same. Tesnion is actually a force while stress is force acting per unit area.

6. What is the Formula of Tension?

Tension is calculated using the formula T = mg + ma