Q 11-01-009NEETNEET 2024Top questionEasy
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:
Answer: (D) $\dfrac{\alpha t}{\beta}$
Terms that are added must have the same dimensions: $[\alpha t^2] = [\beta t]$.
Dividing both sides by $[\beta t]$:
$$\left[\frac{\alpha t}{\beta}\right] = 1$$
So $\dfrac{\alpha t}{\beta}$ is dimensionless.
Solution by Sreeraj P, M.Sc Physics