Question

In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio $1 : 3$. The ratios of unit of length and time are, respectively,

• A. $\frac{1}{3}$, $\frac{1}{9}$
• B. $\frac{1}{9}$, $\frac{1}{3}$
• C. $3, 9$
• D. $9, 3$

Answer 1

Answer: (B)

$\frac{1}{9}$, $\frac{1}{3}$

Answer 2

Length, $l=\frac{v^{2}}{a};$ time, $t=\frac{v}{a}$ $\Rightarrow$ Ratio of unit of length $=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}$ $\Rightarrow$ Ratio of unit of time $=\frac{1}{3}$