Gravitation — Common Mistakes to Avoid — Summary

Confusing altitude and depth formulas: Altitude uses inverse-square ( $gR^2/(R+h)^2$ ); depth uses linear ( $g(1-d/R)$ ). Never swap them. A common NEET trap asks to compare g at $h = R$ and $d = R/2$ — these give $g/4$ and $g/2$ respectively.
Applying the approximate altitude formula beyond its range: $g' \approx g(1 - 2h/R)$ is valid only when $h \ll R$ . For $h = R$ , it gives $g' = -g$ , which is nonsensical. Always use the exact formula for large heights.
Sign error on gravitational PE: $U = -GMm/r$ is negative. Forgetting the negative sign is the most common error. Option (a) " $+GMm/r$ " is wrong; the correct answer is (b) " $-GMm/r$ ".
Mistaking total energy for PE: Total energy $E = -GMm/2r$ ; PE $= -GMm/r$ . PE has twice the magnitude of total energy. These are frequently given as distractors for each other.
Assuming escape velocity depends on body mass: $v_e = \sqrt{2GM/R}$ has no $m$ (body mass). The energy required to escape ( $\frac{1}{2}mv_e^2$ ) does depend on $m$ , but the velocity threshold does not.
Forgetting $v_e = \sqrt{2}\,v_0$ : Students sometimes confuse orbital and escape velocities. Orbital velocity near Earth is $\approx 8$ km/s; escape is $\approx 11.2$ km/s. The ratio is always $\sqrt{2}$ .
Kepler's Second Law direction: The planet moves fastest at perihelion (closest to Sun) and slowest at aphelion (farthest). This is opposite to intuition for students who think "farther = faster."
Geostationary orbit altitude vs radius: The orbit radius is $\approx 42{,}164$ km from Earth's centre, but the altitude above the surface is $\approx 35{,}786$ km. Questions may specify either; don't mix them.
Dimensional formula of G: $[M^{-1} L^3 T^{-2}]$ — note the negative power of M, frequently asked in NEET.