Physics · Gravitation · NEET
No, and this is the most common mix-up. Potential energy (U) belongs to a mass m at a point: U = -GMm/r, measured in joules (J). Potential (V) belongs to the point itself, not to any mass: V = -GM/r, measured in joules per kilogram (J/kg). The link is simple: U = m x V. So potential is potential energy divided by the test mass. Think of V as a property of the location, and U as what a specific object has when you put it there.
We choose the potential to be zero at infinity (very far away). Gravity pulls a mass inward, so as you bring a unit mass from infinity toward M, gravity does positive work and the potential energy drops below zero. Because V = work done per unit mass to bring it from infinity to that point, V comes out negative. The closer you are to M (smaller r), the more negative V becomes. V is largest (closest to zero) at infinity and most negative at the surface.
The SI unit is joule per kilogram (J/kg), because V = potential energy / mass = J / kg. Its dimensional formula is [L^2 T^-2], the same as (velocity)^2. This is a favourite NEET dimension question. Do not confuse it with gravitational field intensity, which has units N/kg or m/s^2 and dimension [L T^-2].
Gravitational potential is a scalar — it has magnitude and sign but no direction. This makes it easier to work with than the gravitational field (a vector). When two or more masses are present, you add their potentials directly using simple algebra with signs: V(total) = V1 + V2 + ... You do not need vectors, unlike the field where you must add arrows.
The gravitational field (intensity) is the negative rate of change of potential with distance: E = -dV/dr. So the field points in the direction where V decreases fastest, i.e. toward the mass. For a point mass, differentiating V = -GM/r gives E = -GM/r^2 (pointing inward). Field is the slope of the potential; potential is the 'height' of the energy landscape per kilogram.
At what height from the surface of earth the gravitational potential and the value of g are -5.4x10^7 J/kg and 6.0 m/s^2 respectively? (Radius of earth = 6400 km)
Two bodies of mass m and 9m are placed a distance R apart. The gravitational potential at the point on the line joining them where the gravitational field is zero is (G = gravitational constant):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
V = -GM/r, where G is the gravitational constant, M is the mass creating the field, and r is the distance from M to the point. V is in J/kg and is always negative (zero at infinity).
It is maximum (least negative, equal to zero) at infinity and minimum (most negative) closest to the mass. As r decreases, V = -GM/r becomes more negative.
Yes. Between two positive masses the potentials are both negative, so their sum is never zero between them; potential is zero only at infinity or (for two-mass systems) at points outside where contributions cancel is not possible for like signs. But the field can be zero at a point between them while the potential there stays negative — a classic NEET trap.
Potential is a scalar (J/kg, V = -GM/r) describing energy per unit mass. Field is a vector (N/kg, E = -GM/r^2) describing force per unit mass. They are related by E = -dV/dr.
It is a convenient reference point. At infinity a mass feels no gravitational pull, so its stored energy is taken as zero. This choice makes all finite-distance potentials negative and simplifies energy and escape-velocity calculations.
