Physics · Gravitation · NEET
mgh only works when h is very small compared to R, because then g stays almost constant. When h = R, the mass moves far from Earth, and gravity becomes weaker as distance grows. The correct method uses the change in gravitational potential energy. PE at surface = -GMm/R. PE at height R (distance 2R from centre) = -GMm/2R. Work done = final PE - initial PE = (-GMm/2R) - (-GMm/R) = GMm/2R. Since g = GM/R^2, GM = gR^2, so W = gR^2 m / 2R = mgR/2. The 'half' comes from gravity weakening over the trip.
Use W = mgh only when the height h is very small compared to Earth's radius R (about 6400 km). For example, lifting a bag 2 metres or a lift going 100 m up. There g barely changes, so mgh is accurate. Once h becomes a big fraction of R (like h = R, or h = R/2), you must use the potential energy formula W = GMm/R - GMm/(R+h).
W = GMm[1/R - 1/(R+h)]. Writing GM = gR^2, this becomes W = mgR^2 [1/R - 1/(R+h)] = mgRh/(R+h). Check: put h = R and you get W = mgR(R)/(2R) = mgR/2. Put a tiny h (h << R) and R+h is about R, giving W = mgh, matching the simple case. This one formula covers every height.
Yes, when the mass is raised slowly (no leftover speed at the top), the work you do against gravity equals the increase in gravitational potential energy: W = U(final) - U(initial). Because gravitational PE is negative and increases (becomes less negative) as you go up, the work done is positive. This is the safe way to solve any 'raise a mass to height h' NEET problem.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
W = mgR/2, where m is the mass, g is surface gravity, and R is Earth's radius. Equivalently W = GMm/2R.
Because mgh assumes constant g. At h = R the mass is far from Earth and gravity is weaker, so you must use the potential energy method, giving mgR/2.
Use W = mgRh/(R+h). With h = R/2, W = mgR(R/2)/(3R/2) = mgR/3.
W = GMm[1/R - 1/(R+h)], which simplifies to W = mgRh/(R+h). It reduces to mgh for small h and mgR/2 for h = R.
Yes. If the mass is raised slowly, all the work you do against gravity is stored as extra gravitational potential energy.
