Answer
a) use center of mass
b) $\frac{25}{24}$
c) $d=\sum_{i=1}^n\frac{l}{2i}$
d) $35$
Work Step by Step
a) $C_{M1}=\frac{1}{2}l$
$C_{M1}=\frac{M(0m)+M(\frac{1}{2}m)}{2M}=\frac{1}{4}l$
$C_{M1}=\frac{M(0m)+2M\frac{1}{4}}{3M}=\frac{1}{6}l$
$C_{M1}=\frac{M(0m)+3M\frac{1}{6}}{4M}=\frac{1}{8}l$
b) $\frac{1}{8}+\frac{1}{6}+\frac{1}{4}+\frac{1}{2}=\frac{25}{24}$
c) $d=\sum_{i=1}^n\frac{l}{2i}$
d) $d=0.5m$ for each half
$\sum_{i=1}^n\frac{0.30m}{2i}>0.5m$
$n=16$
$2\times16+1(top)+2(Base for each side)=35$
