Question

If force $F$, length $L$ and time $T$ are chosen as fundamental quantities, then the dimensional formula for mass is:

• A. $FLT$
• B. $F^{-1}{L}^{-1}{T}^{-2}$
• C. $F^{-2}{L}^{-2}{T}^{-2}$
• D. $F^1{L}^{-1}{T}^2$

Answer 1

Answer: (D)

Step 1: Given that

Fundamental quantities are, Force F, length L and time T.

Step 2: Finding the dimensional formula of mass:

Let,

Mass= k $F^{\alpha }{L}^{\beta }{T}^{\text{γ}}$

Writing the dimensions on both sides we get,

$\left[M^1{L}^0{T}^0\right]={\left[ML{T}^{-2}\right]}^{\alpha }{\left[L\right]}^{\beta }{\left[T\right]}^{\text{γ}}$

$\left[M^1{L}^0{T}^0\right]=\left[M^{\alpha }{L}^{\alpha +\beta }{T}^{-2\alpha +\gamma }\right]$

Comparing the dimensions on both sides, we get

$\alpha =1$

$\alpha +\beta =0$

$\gamma -2\alpha =0$

Solving these equations, we get

$\alpha =1,\beta =-1and\gamma =2$

Thus,

The dimensional formula for mass will be $F^1{L}^{-1}{T}^2$ .

Hence,

Option D) $F^1{L}^{-1}{T}^2$ is the correct option.