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  4. If y = α + β t + γ t2, where y is in m and t in s, the unit of γ is

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Q. If $y = \alpha + \beta t + \gamma t^2$, where y is in m and $t$ in s, the unit of $\gamma$ is

JIPMERJIPMER 2016Physical World, Units and Measurements

Solution:

$y = \alpha + \beta t + \gamma t^2$
According to principle of homogeneity $\gamma\, t^2$ should have the dimensions of $y \, i.e.$,
$\gamma t^2 = [L] $ or $\gamma T^2 = [L]$
$ \gamma = [ LT^{-2}]$
$ \therefore $ Unit of $\gamma$ is m $s^{-2}$.