Question

Given: $\vec{F}=\frac{\vec{a}}{t}+\vec{b}t^{2}$ where symbols have their usual meaning. The dimensions of $a$ and $b$ are, respectively,

• A. $\left[ML^{-1}T^{-1}\right]$ and $\left[MLT^{-4}\right]$
• B. $\left[MLT^{-1}\right]$ and $\left[MLT^{-4}\right]$
• C. $\left[MLT^{-1}\right]$ and $\left[ML\right]$
• D. $\left[MLT^{-1}\right]$ and $\left[ML^{-1}T^{-4}\right]$

Answer 1

Answer: (B)

$\left[a\right]=\left[\vec{a}\right]=\left[\vec{F}t\right]=\left[MLT^{-2}\right]\times\left[T\right]=\left[MLT^{-1}\right]$
$\left[b\right]=\left[\vec{b}\right]=\left[\frac{\vec{F}}{t^{2}}\right]=\left[MlT^{-2}\right] \left[\frac{1}{T^{2}}\right]=\left[MLT^{-4}\right]$