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QNEET-2024-Ph-68: NEET 2024 Physics - Class 11 NEET-2024-Ph-68 Solution: A force defined by $F = t^2 + t$ acts on a particle at a…

A force defined by

F = \alpha t^2 + \beta t

acts on a particle at a given time t. The factor which is dimensionless if

\alpha

and

\beta

are constants is:

\alpha t/\beta

\beta t/\alpha

\alpha\beta t

\alpha/\beta t

Step-by-Step Verified Solution

The force acting on a particle at a given time t

t

t is defined as F = _ t 2 + _ t

F = \alpha t^2 + \beta t

F = _ t 2 + _t , where _

\alpha

_ and _

\beta

_ are constants. We need to determine which factor is dimensionless if _

\alpha

_ and _

\beta

_ are constants. Using the principle of homogeneity of dimensions:

[ F ] = [ _ t 2 ] = [ _ t ] [ _ ] = [ F ] [ t 2 ] and [ _ ] = [ F ] [ t ] _ [ _ ] [ t ] = [ _ ] _ _ t _ = dimensionless