We are given that $M$ is inversely proportional to $g^3$, meaning we can express this relationship as:

$M = \frac{k}{g^3}$

where $k$ is a constant of proportionality.

We are also given that when $g = 2.5$, $M = 24$. We can use this information to find $k$.

Step 1: Find the constant $k$

Substitute $M = 24$ and $g = 2.5$ into the equation:

$24 = \frac{k}{(2.5)^3}$

First, calculate $(2.5)^3$:

$(2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625$

Now substitute this into the equation:

$24 = \frac{k}{15.625}$

Multiply both sides by 15.625 to solve for $k$:

$k = 24 \times 15.625 = 375$

Step 2: Write the formula for $M$ in terms of $g$

Now that we have $k = 375$, substitute this value back into the original equation:

$M = \frac{375}{g^3}$

Thus, the formula for $M$ in terms of $g$ is:

$M = \frac{375}{g^3}$

This is the required formula.

Would you like more details on any specific step?

Here are some related questions to further your understanding:

1. What happens to the value of $M$ if $g$ doubles?
2. If $M = 3$, what is the value of $g$?
3. Can you express $g$ in terms of $M$?
4. How would the formula change if $M$ was inversely proportional to $g^2$ instead of $g^3$?
5. What is the physical meaning of inverse proportionality in real-world problems?

Tip: When solving inverse proportional problems, make sure you properly calculate and use the constant of proportionality, which relates the variables based on given conditions.