A sphere consists of a solid wooden ball of uniform density 800 kg/m3 and radius 0.30 m and is covered with a thin coating of lead foil with area density 20 kg/m2. Calculate the moment of inertia of this sphere about an axis passing through its center.

Solution 74P Step 1: 3 Density of wooden ball w 800 kg/m Density of the lead l= 20 kg/m 2 Radius r = 0.30 m Step 2: Mass of wooden ball M = w× v Where v = 4/3 r 3 3 3 M w 800 kg/m × 4/3 (0.30 m) M w 90.43 kg Mass of lead M = w × v M =w(20 kg/m ) × (4(0.30) ) 2 M w 7.539 kg