Question

A force is given by $F=at+b{t}^2$ where $t$ is time. The dimensions of $a$ and $b$ are

• A. $\left[{\text{MLT}}^{-4}\right]\text{,}\left[{\text{MLT}}^{-2}\right]$
• B. $\left[{\text{MLT}}^{-3}\right]\text{,}\left[{\text{MLT}}^{-4}\right]$
• C. $\left[{\text{ML}}^2{\text{T}}^{-3}\right]\text{,}\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
• D. $\left[{\text{ML}}^2{\text{T}}^{-3}\right]\text{,}\left[{\text{ML}}^2{\text{T}}^{-4}\right]$

Answer 1

Answer: (B)

Dimension of $at$ = Dimension of $F$
$\left[\text{at}\right]=\left[\text{F}\right]$
$\left[\text{a}\right]=\left[\frac{\text{F}}{\text{t}}\right]$
$\left[\text{a}\right]=\left[\frac{{\text{MLT}}^{-2}}{\text{T}}\right]$
$\left[\text{a}\right]=\left[{\text{MLT}}^{-3}\right]$
Dimension of ${\text{bt}}^2=$ Dimension of $F$
$\left[{\text{bt}}^2\right]=\left[\text{F}\right]$
$\left[\text{b}\right]=\left[\frac{\text{F}}{{\text{t}}^2}\right]$
$\left[\text{b}\right]=\left[\frac{{\text{MLT}}^{-2}}{{\text{T}}^2}\right]$
$\left[\text{b}\right]=\left[{\text{MLT}}^{-4}\right]$