You have a teardrop-shaped (2.00-mathrm{kg}) object that has a hook at one end and is (0.28 mathrm{~m})

Question:

You have a teardrop-shaped $2.00-\mathrm{kg}$ object that has a hook at one end and is $0.28 \mathrm{~m}$ long along its longest axis (Figure P15.83). When you try to balance the object on your fingers, it balances when your fingers are $0.20 \mathrm{~m}$ from the hook end. When you hang the object by the hook and set it into simple harmonic motion, it completes 10 cycles in $11 \mathrm{~s}$. What is its rotational inertia $I$ about the hook?

Data from Figure P15.83