The dimensional symbol of tension in a string is expressed as

Analysis

The question asks for the dimensional formula of tension. To solve this, we must recognize that tension is a type of force. In physics, any force (whether it is tension, weight, thrust, or friction) follows the same dimensional rules.

Concept

According to Newton's Second Law of Motion, Force ($F$) is the product of mass ($m$) and acceleration ($a$):

• Mass ($m$): The dimension is represented by [M].
• Acceleration ($a$): Acceleration is the rate of change of velocity with respect to time. Since velocity is distance/time ($L/T$), acceleration is distance/time$^2$ ($L/T^2$). Therefore, the dimension is [L T$^{-2}$].

Solution

1. Since Tension ($T$) is a force, we use the formula: $$\text{Tension} = \text{Mass} \times \text{Acceleration}$$
2. Substitute the dimensions: $$\text{Dimension} = [M] \times [L T^{-2}]$$
3. Combine them: $$\text{Dimension} = [M L T^{-2}]$$

Comparing this result to the given options:

• A: $L T^{-2}$ (This is acceleration)
• B: $M^2 L^{-1} T^{-2}$ (Incorrect)
• C: $M L T^2$ (Incorrect)
• D: $M L T^{-2}$ (Correct)

Tip for JAMB

Whenever you are asked for the dimension of a force-related quantity (like Tension, Weight, Thrust, or Upthrust), always remember the acronym MLT with the exponent -2 on the T. It is a common JAMB favorite!