The effective depth of a simply supported slab can be determined based on the maximum bending moment experienced by the slab. In this case, the maximum bending moment is given as M kg-cm.

To calculate the effective depth, we need to consider the formula for the bending moment of a simply supported slab:

M = (w * L^2) / 8

Where M is the maximum bending moment, w is the uniformly distributed load on the slab, and L is the span length of the slab.

To find the effective depth, we need to rearrange the formula and solve for d (the effective depth):

d = √(8M / w)

Now, let's examine the options given:

Option A: m/100Q
Option B: M/10√Q
Option C: √M/Q
Option D: √M/100Q

It is important to note that in any equation or formula, the units of measurement must be consistent. In this case, the units for M are kg-cm, and the units for d (the effective depth) would be cm.

Let's analyze each option:

Option A: m/100Q
This option does not include the square root of M, which is essential in the formula for calculating the effective depth. Therefore, option A is incorrect.

Option B: M/10√Q
This option includes the square root of M, but it does not include the factor of 8 in the denominator. Therefore, option B is incorrect.

Option C: √M/Q
This option does not include the factor of 8 in the denominator. Therefore, option C is incorrect.

Option D: √M/100Q
This option includes the square root of M and the factor of 8 in the denominator. Therefore, option D is the correct answer.

In conclusion, the effective depth of the slab can be calculated using the formula d = √(8M / w), and the correct option in this case is option D: √M/100Q.