A force defined by F = α t^2 + β t acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is: (1) βt/α (2) αt/β (3) αβt (4) αβ/t

Correct Answer: B — αt/βStep-by-step Solution:Force F has dimensions MLT⁻². The term α t² must have same dimensions, so [α] = MLT⁻⁴. The term β t has same dimensions, so [β] = MLT⁻³. Then αt/β has dimensions (MLT⁻⁴ × T) / (MLT⁻³) = (MLT⁻³)/(MLT⁻³) = dimensionless. Hence αt/β is dimensionless.Key Concepts: Dimensional analysis, homogeneity principle.

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A force defined by F = α t^2 + β t acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is: (1) βt/α (2) αt/β (3) αβt (4) αβ/t

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