Physics · Gravitation · NEET
We choose PE = 0 at infinity (very far from Earth), where gravity does no work. Gravity is an attractive force, so as a mass moves closer to Earth, gravity does positive work and the PE drops below zero. So every real point near Earth has negative PE. The minus sign in U = −GMm/r shows the mass is bound (trapped) by gravity. It is not a mistake; it is how we measure energy from the zero we picked at infinity.
Use U = mgh only for small heights near the surface (h much smaller than Earth's radius R), where g is nearly constant. This gives the CHANGE in PE, not the true value. Use the full formula U = −GMm/r for large distances like satellites, escape velocity, or when h is close to R. Rule for NEET: if the problem mentions a satellite, orbit, escape, or a height comparable to R, use −GMm/r. If it is a ball near the ground, mgh is fine.
The standard reference is infinity. At r = infinity, U = −GMm/r becomes zero. This choice makes the formula clean and is used in all NEET satellite and escape-velocity problems. For the simple mgh form, the reference is usually the ground or the lowest point, which is a different (local) choice. Always check which zero the question is using.
No. Gravity is a conservative force, so the PE depends only on the start and end positions, not the route. Whether you lift a mass straight up or along a curved path, the change in PE is the same, U(final) − U(initial). This is why energy conservation works so cleanly in gravitation problems.
It is the distance from the CENTRE of the Earth, not from the surface. At the surface r = R (Earth's radius). At height h above the surface, r = R + h. A common mistake is to plug in only h; always use R + h for the full formula.
Taking gravitational potential energy at infinity to be zero, the change in PE (final − initial) of a mass m raised to height h above the earth's surface (Earth mass M, radius R) is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The joule (J), same as any energy. In the formula U = −GMm/r, G is in N·m²/kg², masses in kg, and r in metres, giving joules.
Potential energy U is for a specific mass m (unit: joule). Gravitational potential V is energy per unit mass, V = −GM/r (unit: J/kg). So U = mV. Potential describes the field itself; PE describes a particular object placed in it.
It is maximum at infinity, where U = 0. Since all finite points give negative values, zero is the largest possible value. So PE increases (moves toward zero) as you move away from Earth.
It is a scalar. Energy has magnitude but no direction. So you just add the values (with their signs) when several masses are involved.
Choosing infinity as zero gives one clean formula, U = −GMm/r, that works at every distance and matches escape-velocity and satellite equations. Taking the surface as zero only works for small heights and cannot describe satellites.
