Two uniform spherical shells are located such that their centers are along the \(x\) axis in Figure P13.70. The inner shell has mass \(m_{\text {inner }}\) and radius \(R\), and its center is at \(x=0.80 R\). The outer shell has mass \(3.0 m_{\text {inner }}\) and radius \(2.0 R\), and its center is at \(x=0\). What is the magnitude of the vector sum of the gravitational forces exerted by these two shells on an object of mass \(m_{\mathrm{obj}}\) placed \((a)\) at \(x=3.0 R,(b)\) at \(x=1.9 R\), and \((c)\) at \(x=0.90 R\) ?

Data from Figure P13.70

Figure P13.70 2.0R 3.0m inner 0 0.80R R x