PhysicsNEET 2024SI units, dimensions and dimensional analysis

Units and Measurements

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:

Solution

$α t^{2}$ and $β t$ both have the dimensions of force, so $[α t] = [β]$ . Hence $\frac{α t}{β}$ is dimensionless.

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