Two objects of different masses falling freely near the surface of the Moon would

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Correct — C, have same velocity at any instant. "Falling freely" means the only force acting is gravity. Newton's law of gravitation puts the pull on a body of mass m sitting at the Moon's surface at F = GMm/R², where M is the Moon's mass (7.35 × 10²² kg) and R its radius (1,737 km). Newton's second law then gives that body's acceleration as a = F/m = GM/R² — and the falling body's own mass m has cancelled out of the expression entirely. Every object near the lunar surface therefore falls with one and the same acceleration, g on the Moon = 1.62 m/s², roughly one-sixth of Earth's 9.8 m/s². Two objects released together from rest thus satisfy v = u + at with the same u = 0 and the same a, so their speeds are equal at every instant, and by s = ½at² they have also fallen through the same distance. This is not a blackboard argument: it was actually done on the Moon. On 2 August 1971, on Apollo 15's third moonwalk, David Scott held out an aluminium geology hammer of about 1.32 kg in one hand and a falcon feather of about 30 g in the other, released them together in front of the television camera, and they struck the lunar dust at the same moment. On Earth the feather loses that race not because gravity treats it differently but because air drag does — and the Moon has effectively no air, its exosphere sitting near 10⁻¹⁵ of Earth's surface pressure, so free fall there is literally free. One condition the stem leaves implicit is worth naming: equal velocity at any instant follows because the two are falling together from rest; had they been released at different moments they would still share the acceleration but not the speed.

Why the other options are wrong — (a) The intuitive answer, and the one Aristotle taught for nearly two thousand years — heavier things must fall faster. Galileo's insight, confirmed by Newton's algebra, is that the gravitational pull grows in exact proportion to the mass while the resistance to being accelerated (the inertia) grows in exactly the same proportion, so the two scalings cancel and every body accelerates at 1.62 m/s² on the Moon. Different accelerations appear only when a second force such as air drag enters, and on the Moon there is essentially none.  (b) Inertia is measured by mass, and mass is an intrinsic property of a body — it does not change because the body has been moved to the Moon or because it is falling. A 60 kg person carries 60 kg of mass on Earth, on the Moon and in deep space; what changes is weight, the force mg, which drops from about 588 N on Earth to about 97 N on the Moon. Candidates pick this option by silently swapping the word 'weight' for 'inertia'.  (d) The over-correction trap: a candidate who has just remembered that the accelerations are equal assumes the forces must be equal too. They are not. The gravitational force is F = mg, so a 10 kg rock is pulled with 16.2 N while a 1 kg rock is pulled with 1.62 N — a tenfold difference. The accelerations come out equal precisely because the larger force is applied to a proportionately larger inertia, not because the forces are the same.

Concept: Free fall is motion under gravity alone, with every other force — air resistance above all — absent or negligible. Its defining property is that the acceleration it produces is the same for all bodies at a given place, because the gravitational force on a body is proportional to its mass while its resistance to acceleration is measured by that same mass. Formally, the gravitational mass appearing in F = GMm/R² and the inertial mass appearing in F = ma are numerically identical — the weak equivalence principle, tested today to better than one part in 10¹⁵ and later generalised by Einstein into the foundation of general relativity. The consequence is a value of g that belongs to the attracting body, not to the falling one: 9.8 m/s² at Earth's surface, 1.62 m/s² at the Moon's, 3.72 m/s² on Mars, about 24.8 m/s² on Jupiter. Mass, weight and inertia must be kept apart in this topic: mass (kg) is intrinsic, weight (newtons) is the force mg and varies from place to place, and inertia is simply another name for the body's mass in its role of resisting a change of motion.

State PCS 2023 Q21 — Science & Technology PYQ with Answer

State PCS 2023 Q21 — Science & Technology PYQ with Answer