Answer
See answers.
Work Step by Step
a. The axis passes through the oxygen atom, so the oxygen atom contributes no rotational inertia.
The axis is perpendicular to the plane of the molecule. Each hydrogen atom is a distance L from the axis of rotation.
$$I=2m_HL^2=2(1.66\times10^{-27}kg)(0.096\times10^{-9}m)^2$$
$$=3.1\times10^{-47} kg \cdot m^2$$
b. The axis passes through the oxygen atom, so the oxygen atom contributes no rotational inertia.
The axis is in the plane of the molecule. Each hydrogen atom is a distance $L sin 52^{\circ}$ from the axis of rotation.
$$I=2m_H(L \times sin 52^{\circ})^2=2(1.66\times10^{-27}kg)(0.096\times10^{-9}m \times sin 52^{\circ})^2$$
$$=1.9\times10^{-47} kg \cdot m^2$$
