Question

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

• A. $ [ML{{T}^{-3}}] $ and $ [ML{{T}^{-4}}] $
• B. $ [ML{{T}^{-3}}] $ and $ [M{{L}^{2}}{{T}^{-4}}] $
• C. $ [ML{{T}^{-4}}] $ and $ [ML{{T}^{1}}] $
• D. $ [ML{{T}^{-3}}] $ and $ [M{{L}^{2}}{{T}^{-4}}] $

Answer 1

Answer: (A)

Given that $F = at + bt ^{2}$ where $t$ is time.
For this equation to be dimensionally correct, the each term in the right hand side should have the dimensions of $F$
Dimensional formula of $F =\left[ MLT ^{-2}\right]$
$\Rightarrow aT =\left[ MLT ^{-2}\right]$
$\Rightarrow $ Dimension of a is $\left[ MLT ^{-3}\right]$
and $\Rightarrow bT ^{2}=\left[ MLT ^{-2}\right]$
$\Rightarrow $ Dimension of $b$ is $\left[ MLT ^{-4}\right]$