Gravitational Potential Energy

The acceleration due to gravity at height from the surface of the earth is given by the formula: where is the acceleration due to gravity on the surface of the earth and is the radius of the earth. Here, (height above the earth's surface), so the formula becomes: Hence, the value of the acceleration due to gravity at a height of from the surface of the earth is .

The gravitational potential energy at a point outside the system is the sum of the potentials due to both the sphere and the shell. After calculating the potential energies and applying the principle of superposition, we find the correct value to be . Thus, the correct answer is option (1).