A) 42.7 kg m^2
We can consider Olga has a uniform rod, rotating about one of her end, with her mass distributed along the body. Therefore, her moment of inertia is given by
[tex]I=\frac{1}{3}mL^2[/tex]
where
m = 50.0 kg is the mass
L = 1.6 m is the length of Olga's body
Substituting into the equation, we find
[tex]I=\frac{1}{3}(50.0 kg)(1.6 m)^2=42.7 kg m^2[/tex]
B) 10.6 kg m^2
The problem is the same as before, however this time the length of Olga's body is just half the length she had before:
[tex]L=\frac{1.6 m}{2}=0.8 m[/tex]
Therefore, her moment of inertia will be
[tex]I=\frac{1}{3}(50.0 kg)(0.8 m)^2=10.6 kg m^2[/tex]
