A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:
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Question

A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:

G1 Physics · Accepted Answer

Step 1: Since αt² and βt both have dimensions of force, [α]=[F T⁻²] and [β]=[F T⁻¹]. Step 2: Therefore [αt/β]=1, so αt/β is dimensionless. Final: Option A.