Q. If the unit of velocity is run, the unit of time is second and unit of force is strength in a hypothetical system of unit. In this system of unit, the unit of mass is (strength)$^{x}$ (second)$^{y}$ (run)$^{z}$ Find the value of $\frac{y}{x}$

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Solution:

$\because F =m a$
$\Rightarrow m =\frac{F}{a}=(\text { Force })+\frac{\text { Change in velocity }}{\text { Time }}$
$=\frac{\text { Force } \times \text { Time }}{\text { Change in velocity }}$
$=(\text { strength })(\sec o)(\text { run })^{-1}$
Thus, $x=1, y=1$ and $x=-1$
$\therefore \frac{y}{x}=1$

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