Question

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 $\frac{y}{x}$

• A. $3$
• B. $5$
• C. $6$
• D. $1$

Answer 1

Answer: (D)

$\because F=ma$

$\Rightarrow m=\frac{F}{\alpha }=\left(\text{Force}\right)/\frac{\text{Change in velocity}}{\text{Time}}$

$=\frac{\text{Force × Time}}{\text{Change in velocity}}$

=(strength)(s)(run) ${}^{-1}$

Thus, $x=1,y=1$ and $z=-1$

$\therefore \frac{y}{x}=1$