Physics · Gravitation · NEET
Yes. Both fall with the same g = 9.8 m/s². Earth pulls the heavy stone with more force (F = mg), but the heavy stone also needs more force to accelerate. When you divide force by mass (a = F/m), the mass cancels out, so both get the same acceleration. This is why a coin and a feather fall together in vacuum. NEET loves this idea.
Start from Newton's law: the force on a body of mass m near Earth is F = GMm/R². By Newton's second law F = ma. Setting them equal: ma = GMm/R². The small m cancels on both sides, giving a = g = GM/R². Only Earth's mass M and radius R are left. So g depends on the planet, not on what is falling.
g is the physical quantity 'acceleration due to gravity'. 9.8 m/s² is just its value on Earth's surface. On the Moon g is about 1.6 m/s², on Jupiter it is larger. So 9.8 is one special value of g, only for Earth's surface. Do not treat 9.8 as a fixed constant like G.
Yes. Since g = GM/R², a planet with a different mass M or radius R has a different g. A planet with more mass but the same radius has a larger g. A planet with the same mass but bigger radius has a smaller g. Big G stays the same everywhere; only g changes.
Write the gravitational force on mass m at Earth's surface: F = GMm/R². This force produces free-fall acceleration, so F = mg. Equate them: mg = GMm/R². Cancel m from both sides to get g = GM/R². This single line connects Newton's universal law to everyday free fall.
The mass of a planet is 1/10th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
About 9.8 m/s² (often rounded to 9.81 m/s²). This is how much the speed of a freely falling body increases every second, ignoring air resistance.
g is an acceleration, so its SI unit is metre per second squared (m/s²). It can also be written as newton per kilogram (N/kg), because g = force per unit mass; both units are equal.
g is a vector. It has magnitude (about 9.8 m/s²) and direction (pointing towards the centre of the Earth, i.e. downward).
g = GM/R², where G is the universal gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²), M is the mass of the Earth, and R is the radius of the Earth.
g is the base of the whole Gravitation chapter. Variation of g with height and depth, weight of a body, escape velocity, and satellite motion all start from g = GM/R². Almost every year NEET asks a numerical that uses this formula.
