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 $F=at+b{t}^2$ 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 $F=\left[ML{T}^{-2}\right]$
$\Rightarrow aT=\left[ML{T}^{-2}\right]$
$\Rightarrow$ Dimension of a is $\left[ML{T}^{-3}\right]$
and $\Rightarrow b{T}^2=\left[ML{T}^{-2}\right]$
$\Rightarrow$ Dimension of $b$ is $\left[ML{T}^{-4}\right]$