1. Use the orbital period relation

For a moon orbiting a planet in a circular orbit,

$T^2 = \frac{4\pi^2 r^3}{GM}$

So the mass of Mars is

$M = \frac{4\pi^2 r^3}{G T^2} = \left(\frac{4\pi^2}{G}\right)\frac{r^3}{T^2}$

Given,

$\frac{4\pi^2}{G} = 6\times 10^{11}$

2. Convert the given quantities to SI units

Orbital radius:

$r = 9.0\times 10^3\ \text{km} = 9.0\times 10^6\ \text{m}$

Time period:

$T = 7\ \text{h}\ 30\ \text{min} = 7.5\ \text{h}$

$T = 7.5\times 3600 = 27000\ \text{s} = 2.7\times 10^4\ \text{s}$

3. Substitute into the formula

First compute $r^3$:

$r^3 = (9.0\times 10^6)^3 = 9^3\times 10^{18} = 729\times 10^{18} = 7.29\times 10^{20}$

Now compute $T^2$:

$T^2 = (2.7\times 10^4)^2 = 7.29\times 10^8$

Thus,

$\frac{r^3}{T^2} = \frac{7.29\times 10^{20}}{7.29\times 10^8} = 10^{12}$

Hence,

$M = 6\times 10^{11}\times 10^{12} = 6\times 10^{23}\ \text{kg}$

4. Match with the options

$M = 6.00\times 10^{23}\ \text{kg}$

So the correct option is D.