Question

A force is given by $F=at+bt^{2}$ 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 $F$
$\left[\text{bt}^{2}\right] = \left[\text{F}\right]$
$\left[\text{b}\right] = \left[\frac{\text{F}}{\text{t}^{2}}\right]$
$\left[\text{b}\right] = \left[\frac{\text{MLT}^{- 2}}{\text{T}^{2}}\right]$
$\left[\text{b}\right] = \left[\text{MLT}^{- 4}\right]$