Question

What is the ratio of C.G.S. to M.K.S. unit of acceleration?

Answer 1

Step 1: Given:

C.G.S. acceleration,$a_1=1\frac{\text{cm}}{{\text{s}}^2}$.

M.K.S. acceleration, $a_2=1\frac{\text{m}}{{\text{s}}^2}$.

Step 2:Write an expression of ratio of accelerations as:

$R=\frac{a_1}{a_2}$

Step 3: Substitute $1\frac{\text{cm}}{{\text{s}}^2}$ for $a_1$ and $1\frac{\text{m}}{{\text{s}}^2}$ for $a_2$ in expression of ratio:

$$\begin{gathered} R=\frac{{\displaystyle \frac{1\left|\text{cm}\right|\times {\displaystyle \frac{{10}^{-2}\text{m}}{\left|\text{cm}\right|}}}{{\text{s}}^2}}}{1{\displaystyle \frac{\text{m}}{{\text{s}}^2}}} \\ =\frac{1}{100} \end{gathered}$$

Hence, ratio of C.G.S. to M.K.S. unit of acceleration is $\frac{1}{100}$.