Physics · Gravitation · NEET
No. Gravitational potential V is the energy per unit mass at a point due to a source mass M, so V = -GM/r and its unit is J/kg. Gravitational potential energy U is the energy of a specific mass m sitting at that point, so U = -GMm/r and its unit is joule (J). The link is simple: U = m x V. Potential describes the field itself; potential energy describes what a body has in that field.
Potential is made a property of the field alone, not of any test body. By dividing the work done by the mass carried (V = W/m for bringing unit mass from infinity), the value depends only on the source mass M and distance r. This lets you compare points in space without picking a test mass. To get the energy of an actual body, you just multiply back: U = m x V.
Gravitational potential V has unit J/kg (= m^2/s^2) and dimensional formula [L^2 T^-2]. Gravitational potential energy U has unit joule (J) and dimensional formula [M L^2 T^-2]. Notice U carries an extra mass dimension [M] compared to V, exactly because U = m x V.
Zero is defined at infinity. As a mass is brought from infinity toward another mass, gravity does positive work, so the stored energy drops below zero. Both V = -GM/r and U = -GMm/r are therefore negative and become less negative (rise toward zero) as r increases. The negative sign shows the system is bound.
Use U = m x V. If a problem gives the potential V at a point (in J/kg) and asks for the energy of a mass m placed there, multiply: U = m x V. Reverse it to find V from U: V = U/m. In the 2016 NEET question, V and g are given at a height, and dividing |V|/g = (R+h) locates the point without ever needing m.
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)
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 (radius R) is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Gravitational potential V = -GM/r is energy per unit mass (J/kg) and depends only on the source; potential energy U = -GMm/r is the energy of a body of mass m (J). They are linked by U = m x V.
No. V depends only on the source mass M and distance r. That is exactly why it is defined per unit mass. Only the potential energy U depends on the test mass m.
Both are scalars. Neither has direction. Only gravitational field intensity (E = -GM/r^2) and gravitational force are vectors.
Both are zero at infinity by the standard reference choice. They are negative everywhere else and increase toward zero as r increases.
NEET regularly mixes V and U in numerical and dimension-matching questions (2016, 2019, 2022). Picking the wrong formula or unit (J vs J/kg) is a common way marks are lost, so knowing U = m x V is essential.
