Question
The dimensional formula of force:
This question was previously asked in
RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)
The correct answer is
$[\text{MLT}^{-2}]$
Deriving the Dimensional Formula of Force
To find the dimensional formula of force, we use its definition and the dimensions of the quantities involved.
Fundamental Relation
Force is defined as the product of mass and acceleration:
$F = m \times a$
Dimensions of Components
- The dimensional formula for mass ($m$) is [M].
- Acceleration ($a$) is the rate of change of velocity, and its dimensional formula is [LT-2] (Length divided by Time squared).
Calculating Force Dimension
Substitute the dimensions of mass and acceleration into the formula for force:
$[F] = [m] \times [a]$
$[F] = [\text{M}] \times [\text{LT}^{-2}]$
$[F] = [\text{MLT}^{-2}]$
Conclusion
The dimensional formula of force is [MLT-2].
This corresponds to Option 2.
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