Question

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

• A. $\left[ MLT ^{-1}\right]$ and $\left[ MLT ^{0}\right]$
• B. $\left[ MLT ^{-3}\right]$ and $\left[ ML^{2}T ^{4}\right]$
• C. $\left[ MLT ^{-4}\right]$ and $\left[ MLT ^{1}\right]$
• D. $\left[ MLT ^{-3}\right]$ and $\left[ MLT ^{-4}\right]$

Answer 1

Answer: (D)

$\left[ MLT ^{-3}\right]$ and $\left[ MLT ^{-4}\right]$

Answer 2

Force $F=a t +b t^{2}$
From principle of homogeneity,
Dimensions of $a t=$ dimensions of $F$
$\therefore$ Dimensions of $a=\frac{[F]}{[t]}=\frac{\left[ MLT ^{-2}\right]}{[ T ]}$
$=\left[ MLT ^{-3}\right]$
Similarly, dimensions of
$b=\frac{[F]}{\left[t^{2}\right]}=\frac{\left[ MLT ^{-2}\right]}{\left[ T ^{2}\right]}=\left[ MLT ^{-4}\right]$