Free fall and lunar gravity: basic meaning

Free fall means motion under gravity alone, with other forces such as air drag neglected. Near the Moon’s surface, a freely falling object experiences approximately 1.62 m/s² downward gravitational acceleration. NASA gives this surface value and contrasts it with Earth’s approximately 9.8 m/s².

The Moon has an extremely thin exosphere, not a substantial atmosphere like Earth’s. Air resistance is negligible for a simple near-surface school-physics drop, allowing light and heavy objects to accelerate almost identically when released with equal initial conditions. The Moon’s surface gravity is about one-sixth of Earth’s, but it is definitely not zero.

For BPSC and State PSC general-science questions, it is essential to distinguish acceleration, velocity, gravitational force, weight, mass and inertia. Falling objects with different masses experience different gravitational force magnitudes, yet the same acceleration in the ideal free-fall model.

Why different masses fall with the same acceleration

Newton’s gravitational force on an object near a celestial surface can be written F = mg, while Newton’s second law says F = ma. For free fall under gravity alone, equating the expressions gives ma = mg and therefore a = g. The object’s mass cancels.

Imagine two stones with masses 1 kg and 5 kg released together at rest near the Moon’s surface. The gravitational forces are about 1.62 N and 8.10 N respectively, but both undergo 1.62 m/s² downward acceleration. The heavier stone feels five times the gravitational force and has five times the inertia, leaving the same ratio of force to inertial mass.

This conclusion does not require the stones to have equal weight. It does require that non-gravitational forces are negligible and their initial conditions are comparable. Air drag makes everyday falls on Earth more complicated, even though gravity itself accelerates objects nearly equally there too.

Mass, weight and inertia on the Moon

A person who has a mass of 60 kg on Earth still has a mass of 60 kg on the Moon. Their weight is approximately 588 N on Earth and 97.2 N on the Moon. This is why astronauts can make larger hops and objects fall more slowly in a given local experiment, even though carrying or accelerating the same equipment still requires overcoming its inertia.

Equations of uniformly accelerated free fall

Take downward as positive, use a near-surface constant g and neglect drag. The standard equations are v = u + gt, s = ut + ½gt² and v² = u² + 2gs, where u is initial downward velocity, v is later downward velocity, t is time and s is downward displacement.

For an object simply dropped from rest, u = 0, giving v = gt, s = ½gt², t = √(2s/g) and v = √(2gs). These are ideal kinematics expressions, not formulas for escape velocity or for falling over vast planetary distances where gravity varies substantially.

Solved numerical 1: fall from 5 metres

Question: How long will a rock dropped from rest take to reach the Moon’s surface from a height of 5 m? Assume constant g_Moon = 1.62 m/s².

Solution: s = ½gt², so t² = 2s/g = 10/1.62 ≈ 6.173. Hence t ≈ 2.48 s. The impact speed is v = gt ≈ 1.62 × 2.48 = 4.02 m/s downward.

If a second object with different mass is released simultaneously at the same height and from rest, it will reach the surface at essentially the same time in the no-drag approximation. Its weight will differ, but the calculated acceleration and drop time will not.

Solved numerical 2: distance after two seconds

Question: What displacement does an object undergo when freely falling for 2 seconds on the Moon, starting from rest?

Use s = ½gt² = 0.5 × 1.62 × 2² = 3.24 m downward. The downward speed after 2 seconds is v = 1.62 × 2 = 3.24 m/s. The two numerical values match here by coincidence of the chosen time and units; displacement and speed are physically different quantities.

For a classroom examination, always include units. Acceleration uses m/s²; speed uses m/s; displacement uses metres; weight uses newtons. An answer of ‘3.24’ alone may hide the confusion.

Solved numerical 3: weight comparison

Question: Calculate the weight of a 12 kg object on the Moon and on Earth, taking g_Moon = 1.62 m/s² and g_Earth = 9.8 m/s².

Moon: W = 12 × 1.62 = 19.44 N. Earth: W = 12 × 9.8 = 117.6 N. Its mass remains 12 kg in both places. The weight ratio 19.44/117.6 ≈ 0.165, which agrees with the approximately one-sixth gravity comparison.

If the object were dragged along a horizontal floor, its frictional force could also change because its normal force is lower. However, the body’s resistance to acceleration is still connected with its unaltered inertial mass.

Solved numerical 4: horizontal or upward motion

Not every freely moving object begins from rest. For a rock thrown vertically upward on the Moon, gravity acts downward during its entire flight, even while it is rising. If initial upward speed is u, the maximum rise in height relative to release point is H = u²/(2g) in the constant-g approximation.

Example: A rock is thrown upward at 8.1 m/s. Time to the highest point is u/g = 8.1/1.62 = 5 s. The height gained is 8.1²/(2 × 1.62) = 20.25 m. If it returns to the same level and conditions remain ideal, the total flight time is about 10 seconds.

At the highest point the instantaneous vertical velocity is zero, but the downward acceleration is not zero. This is a standard gravity misconception.

When do two objects have the same velocity?

Two objects released from rest at the same instant, from the same location in the same uniform gravitational field and with negligible drag, have equal velocities at each later instant. If both begin with the same initial velocity u, the equality still holds because v = u + gt applies to each.

But same gravitational acceleration does not guarantee identical velocities under every possible initial condition. If one stone is thrown down at 3 m/s while the other is dropped from rest, their velocities remain different even though their acceleration is the same. If the objects are released at different times, comparing ‘at any instant’ also requires care.

This qualification makes the original BPSC free-fall question scientifically precise: its keyed answer assumes a simultaneous drop with equal initial conditions. Exam questions sometimes leave such assumptions implicit.

Apollo 15: hammer and feather experiment

During the Apollo 15 mission in 1971, astronaut David Scott simultaneously released a geological hammer and a feather near the lunar surface. NASA’s recorded demonstration shows them striking the surface essentially together. With practically no aerodynamic drag, the light feather and heavy hammer followed gravity-driven motion with nearly the same acceleration.

On Earth, a feather falls slowly in ordinary air because its drag force is large relative to its weight. A hammer experiences a much smaller relative drag effect. If both were released in an adequate vacuum chamber on Earth, the ideal free-fall times would also match. The Moon’s key advantage for the demonstration is its negligible atmospheric resistance.

The experiment illustrated a principle associated with Galileo and the equivalence of gravitational and inertial response; it did not prove that heavier and lighter objects have equal gravitational forces.

Why the Moon has weaker gravity

The surface gravitational acceleration of a spherical body is approximately g = GM/R², where G is the universal gravitational constant, M is the body’s mass and R is its radius. The Moon has much less mass than Earth, so its surface gravity is substantially lower. Differences in radius also matter because the field depends on the square of distance from the centre.

NASA’s Moon fact sheet lists lunar radius at roughly 1,737 km, surface gravity about 1.62 m/s² and escape velocity about 2.38 km/s. These are useful reference values but involve different physics: escape speed requires considering gravitational energy over large distances, not merely setting v = gt for a few seconds.

Local variations in lunar gravity arise from irregular mass distributions and topography, so 1.62 m/s² is an average near-surface approximation rather than an infinitely precise constant everywhere.

Earth versus Moon: same physics, different values

For the same height in ideal conditions, the time ratio is t_Moon/t_Earth = √(g_Earth/g_Moon) ≈ √6 ≈ 2.45. Similarly, final speed from the same height is lower on the Moon because v = √(2gh).

Gravity, orbiting satellites and weightlessness

Weightlessness in orbit does not mean that gravity has disappeared. A spacecraft and its occupants can be in continuous free fall around the attracting body, so they experience little supporting force relative to each other. This produces apparent weightlessness.

A satellite’s orbital trajectory is curved because gravity changes the direction of its velocity. Near the lunar surface an astronaut or dropped rock follows a local trajectory under lunar gravitational force. The phrase ‘free fall’ applies whenever gravity is effectively the only force, even if an object is moving sideways in orbit rather than straight down.

In a typical BPSC short question, however, ‘two objects in free fall near the Moon’s surface’ asks about acceleration due to gravity, not the equations of orbital motion.

Preserved BPSC 69th Prelims Question 21

Question as recorded in the existing CrackTarget post: Two objects of different masses falling freely near the surface of the Moon would: (A) have different accelerations; (B) undergo a change in their inertia; (C) have same velocity at any instant; (D) experience forces of same magnitude.

Original keyed answer: (C). Under the intended assumption that the objects are released together with the same initial velocity and experience negligible drag, they acquire the same downward velocity at every equal elapsed time. Option A is wrong because both accelerate at approximately 1.62 m/s². B is wrong because inertial mass does not change merely by falling. D is wrong because gravitational force F = mg differs with mass.

Strictly speaking, option C requires matched initial conditions. This page makes that implied assumption explicit so the physics remains correct beyond the exam’s expected answer.

Quick revision: 12 exam traps

1. Mass is measured in kilograms and is essentially unchanged between Earth and Moon.
2. Weight is a force, measured in newtons; it depends on local g.
3. Moon’s surface g is about 1.62 m/s², not zero.
4. Different masses experience the same free-fall acceleration when drag is negligible.
5. Greater mass gives greater gravitational force but also greater inertia.
6. The Moon has a tenuous exosphere, not a dense atmosphere.
7. The Apollo 15 hammer and feather landed almost simultaneously.
8. Two objects need matching initial velocities for their velocities to stay equal.
9. From rest: s = ½gt² and v = gt.
10. At the top of a vertical throw, velocity can be zero while acceleration is still downward.
11. Same-height Moon free fall takes about 2.45 times the ideal Earth time.
12. Orbiting astronauts may be in free fall even while gravity remains strong enough to sustain orbit.

25 original lunar-gravity MCQs with explanations

Try conceptual and numerical questions before revealing each answer.

Frequently asked questions

Why do a feather and hammer fall together on the Moon?

Both receive nearly the same gravitational acceleration and aerodynamic drag is negligible.

Does an object’s mass change on the Moon?

No. Its inertial mass stays the same; its weight is lower because lunar gravity is weaker.

What is the formula for fall time from rest?

For a small height with constant g, t = square root of (2h/g).

Do different masses experience identical gravitational force?

No. Near the surface F=mg, so a heavier mass experiences greater force but also greater inertia.

Do two free-falling objects always have exactly the same velocity?

Only with matching initial conditions and under the same ideal acceleration. Equal acceleration alone does not imply equal velocity.

Who demonstrated the hammer and feather drop?

Astronaut David Scott on Apollo 15 in 1971.