Question

If $F$ denotes force and t time, then in equation $F=a{t}^{-1}+b{t}^2$ , the dimensions of $a$ and $b$, respectively are

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

Answer 1

The correct option is D

$\left[ML{T}^{-1}\right]$ and $\left[ML{T}^{-4}\right]$

Explanation for the correct option:

Find the dimensions of $a$ and $b$:

As we know,

$a{t}^{-1}=\left[ML{T}^{-2}\right]$

$\Rightarrow$$a=\frac{\left[ML{T}^{-1}\right]}{t^{-1}}$

$\mathbf{\therefore }\mathit{a}\mathbf{}\mathbf{=}\mathbf{}\left[ML{T}^{-1}\right]$

Also,

$b{t}^{-2}=\left[ML{T}^{-2}\right]$

$\Rightarrow$$b=\frac{\left[ML{T}^{-2}\right]}{t^{-2}}$

$\mathbf{\therefore }\mathit{b}\mathbf{}\mathbf{=}\mathbf{}\left[ML{T}^{-4}\right]$

Hence, Option ‘D’ is Correct.