Question

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

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

Answer 1

Answer: (B)

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

Given, $\frac{\left[v_1\right]}{\left[v_2\right]}=\frac{1}{3}$

Here, $\left[a_1\right]=\left[a_2\right]$ or $\left[v_1{T}_1^{-1}\right]=\left[v_2{T}_2^{-1}\right]$ ( as $a=\frac{dv}{dt}$)

$\frac{T_1}{T_2}=\frac{v_1}{v_2}=\frac{1}{3}$

$\frac{\left[L_1{T}_1^{-1}\right]}{\left[L_2{T}_2^{-1}\right]}=\frac{1}{3}$ as $\left[v\right]=\left[L{T}^{-1}\right]$

$\frac{L_1}{L_2}=\frac{1}{3}\times \frac{\left[T_1\right]}{\left[T_2\right]}=1/3\times 1/3=1/9$