Question

If length L, mass M and force F are taken as fundamental quantities then the dimensions of time will be :

• A. $M^{\frac{1}{2}}{L}^{\frac{1}{2}}{F}^{-\frac{1}{2}}$
• B. $M^{-\frac{1}{2}}{L}^{\frac{1}{2}}{F}^{\frac{1}{2}}$
• C. $M^2{L}^2{T}^{-2}$
• D. $ML{F}^{\frac{1}{2}}$

Answer 1

The correct option is A $M^{\frac{1}{2}}{L}^{\frac{1}{2}}{F}^{-\frac{1}{2}}$

We are given that force $F$, length $L$, and mass $M$ are the fundamental quantities of time $T$ and hence we put,
$T=F^x{L}^y{M}^z$
Substituting their dimensions we have
$\left[T\right]=\left[M^x{L}^x{T}^{-2x}\right]L^y{M}^z$
Applying principle of homogeneity of dimensions we have
$1=-2x$ or $x=\frac{-1}{2}$,
$y=\frac{1}{2}$,
$z=\frac{1}{2}$,
$\therefore$ dimension of time becomes $M^{\frac{1}{2}}{L}^{\frac{1}{2}}{F}^{\frac{-1}{2}}$