CALC? A sphere with radius R = 0.200 m has density ? that decreases with distance r from the center of the sphere according to ? = 3.00 X 10 kg/m3 – (9.00 X 103 kg/m4)r. (a) Calculate the total mass of the sphere. (b) Calculate the moment of inertia of the sphere for an axis along a diameter.

Solution 99P Step 1: Data given Radius of sphere R = 0.200 m 3 3 3 4 Density = 3.00 × 10 kg /m (9 × 10 kg /m )r We need to find the mass of the sphere This is given by dm = × dv 3 But we know v = (4/3)r Thus we get dv = 4r dr 0 3 3 3 4 4 m = (.200 m) 3.00 × 10 kg /m (9 × 10 kg /m )r × 4r dr 0 Substituting values we get m = 55.3 kg Thus we have mass of sphere as 55.3 kg