Question

If velocity $\left[\text{V}\right]$ time $\left[\text{T}\right]$ and force $\left[\text{F}\right]$ are chosen as the base quantities, the dimensions of the mass will be

• A. $\left[\text{F}\text{V}{\text{T}}^{-1}\right]$
• B. $\left[\text{F}{\text{T}}^2\text{V}\right]$
• C. $\left[\text{F}{\text{T}}^{-1}{\text{V}}^{-1}\right]$
• D. $\left[\text{F}\text{T}{\text{V}}^{-1}\right]$

Answer 1

The correct option is D $\left[\text{F}\text{T}{\text{V}}^{-1}\right]$

According to Newton’s second law of motion, force is given by,
$F=ma$
where $m$ denotes mass and $a$ denotes acceleration

Applying dimensional analysis
$\left[\text{F}\right]=\left[\text{m}\right]\left[\text{a}\right]...\left(i\right)$

We know that acceleration is defined as rate of change of velocity
i.e $a=\frac{\text{velocity}}{\text{time}}=\frac{V}{T}$

Dimensional formula for acceleration is $\left[\text{a}\right]=\frac{\left[\text{V}\right]}{\left[\text{T}\right]}...\left(ii\right)$

By substituting $\left(ii\right)$ in $\left(i\right)$
$\left[\text{F}\right]=\left[\text{m}\right]\frac{\left[\text{V}\right]}{\left[\text{T}\right]}$
$\left[\text{m}\right]=\left[\text{F}\right]\frac{\left[\text{T}\right]}{\left[\text{V}\right]}$
$\left[\text{m}\right]=\left[\text{F}\text{T}{\text{V}}^{-1}\right]$