a$.$ A clever trick is to make the problem dimensionless by dividing all lengths by $a.$ This gives an

equivalent problem with a beam of length $\frac{L}{a}$ and a width and height of $1.$ For the dimensionless

problem, determine an expression for the location of the neutral axis. Note that there is only

one location of the neutral axis, so provide only one answer.

Hint: This is a composite beam problem; if you are not familiar, look at an example in a

mechanics of materials textbook.

b$.$ Verify that your answer for part a is reasonable for $n=4.$

c$.$ For arbitrary $n$ and $a=1,$ verify that the beam is in force equilibrium.

Hint: Make a cut through the beam and draw a FBD$.$ Notice that there is no force on the free

end of the FBD$.$ On the cut end of the FBD recall that $F={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dA.$