1. Use the condition for normal adjustment

For a refracting telescope in normal adjustment:

• the final image is formed at infinity,
• so the separation between objective and eyepiece is

$L=f_o+f_e$

Given:

$L=30\text{ cm}$

Hence,

$f_o+f_e=30 \quad ...(1)$

2. Use angular magnification formula

For a refracting telescope in normal adjustment, angular magnification is

$M=\frac{f_o}{f_e}$

Given:

$M=2$

So,

$\frac{f_o}{f_e}=2$

$f_o=2f_e \quad ...(2)$

3. Solve the two equations

Substitute equation (2) into equation (1):

$2f_e+f_e=30$

$3f_e=30$

$f_e=10\text{ cm}$

Therefore,

$f_o=2\times 10=20\text{ cm}$

4. Match with the options

The focal length of the objective is:

$\boxed{20\text{ cm}}$

So the correct option is A.