Question

If force $F$, length $L$ and time $T$ are taken as fundamental units, the dimensional formula for mass will be

• A. $\left[F{L}^{-1}{T}^2\right]$
• B. $\left[FL{T}^{-2}\right]$
• C. $\left[F{L}^{-1}{T}^{-1}\right]$
• D. $\left[F{L}^5{T}^2\right]$

Answer 1

The correct option is A $\left[F{L}^{-1}{T}^2\right]$

$\text{Step 1: Expression for mass}$

From Newton's second law, we can write

$\sum F=ma$

If $\sum F=F$

$\Rightarrow m=\frac{F}{a}$

$\text{Step 2: Dimensional formula}$

Unit of acceleration $a$ $\to$ $m/s^2$

$\Rightarrow$ Dimensional formula of $a$ will be $\left[L{T}^{-2}\right]$

$\Rightarrow$ Dimensional formula of $m$ will be

$m\equiv \frac{\left[F\right]}{\left[L{T}^{-2}\right]}\equiv \left[F{L}^{-1}{T}^2\right]$

Hence option $A$ is correct.