A force defined by F = at^2 + bt acts on a particle at a given time t . The factor which is dimensionless, if a and b are constants, is: - Physics MCQ NEET (UG) 2024 2026 | ExamTest.live

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A force defined by F = a t^{2} + b t acts on a particle at a given time t . The factor which is dimensionless, if a and b are constants, is:

Solution & Step-by-step Explanation

According to the principle of homogeneity: [F] = [a t^{2}] = [b t] [a] = \frac{[ F ]}{[ t ^{2} ]} = M L T^{- 4} [b] = \frac{[ F ]}{[ t ]} = M L T^{- 3} Let's check the ratio \frac{a t}{b} : Dimensions of \frac{a t}{b} = \frac{( M L T ^{- 4} ) \cdot T}{M L T ^{- 3}} = \frac{M L T ^{- 3}}{M L T ^{- 3}} = [M^{0} L^{0} T^{0}] Therefore, \frac{a t}{b} is dimensionless.

Try it yourself before checking the explanation above.

A force defined by F = a t^{2} + b t acts on a particle at a given time t . The factor which is dimensionless, if a and b are constants, is:

\frac{t \cdot b}{a}

\frac{a t}{b}

ab t

\frac{t}{ab}

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