Answer
a) $d=\frac{25}{24}=1.042L$
b) stay the same
Work Step by Step
(a) We know that
$S_1=\frac{L}{2}$
$2mgS_2=mg(\frac{L}{2})$
$\implies S_2=\frac{L}{4}$
and $3mgS_3=2mgS_2$
$\implies S_3=\frac{L}{6}$
$4mgS_4=3mgS_3$
$\implies S_4=\frac{L}{8}$
Now we can find the total length as
$d=S_1+S_2+S_3+S_4$
$\implies d=\frac{L}{2}+\frac{L}{4}+\frac{L}{6}+\frac{L}{8}$
$\implies d=\frac{25}{24}=1.042L$
(b) We know that if the mass were increased then the answer would stay the same because mass cancels in each of the equations that are used to find the individual lengths.
