You're rolling solid rubber balls on the kitchen floor. Ball 1 has a density of \(1.00 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\) and a radius of \(25.0 \mathrm{~mm}\). Ball 2 has an unknown density and a radius of \(40.0 \mathrm{~mm}\) and is initially at rest. You roll ball 1 at an initial speed of \(3.00 \mathrm{~m} / \mathrm{s}\), and the two balls collide head-on. Ball 1 reverses direction and comes back to you at \(2.00 \mathrm{~m} / \mathrm{s}\), and after the collision, the speed of ball 2 is \(1.00 \mathrm{~m} / \mathrm{s}\). With the positive \(x\) axis in the direction of ball 1 's initial motion, what are \((a)\) the magnitudes of the initial and final momenta of ball \(1,(b)\) the initial and final momenta of ball 2 , and (c) the density of ball 2?