Physics

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


ANSWER

$$ M^{\frac{1}{2}}L^{\frac{1}{2}}F^{-\frac{1}{2}} $$


SOLUTION
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
$$\left[T\right]=\left[M^xL^xT^{-2x}\right]L^{y}M^{z}$$
Applying principle of homogeneity of dimensions we have
$$1=-2x$$ or $$x=\dfrac{-1}{2}$$,
$$y= \dfrac{1}{2}$$,
$$z= \dfrac{1}{2}$$,
$$\therefore$$ dimension of time becomes $$M^{\frac{1}{2}} L^{\frac{1}{2}}F^{\frac{-1}{2}} $$ 
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