An object is dropped from a height onto the floor. Which one of the following remains uniform as it falls?
- (a)Its acceleration
- (b)Its momentum
- (c)Its kinetic energy
- (d)Its potential energy
Correct — A, Its acceleration. Once the object leaves the hand, only its weight acts on it, and Newton's second law then gives an acceleration equal to the weight divided by the mass — that is, g, which cancels the mass out entirely. Near the ground g is about 9.8 metres per second squared and stays that value all the way down, so the acceleration is the one quantity in the list that does not change. Everything else does. The speed rises steadily, so the momentum rises with it and the kinetic energy rises as the square of the speed, while the potential energy falls by exactly as much as the kinetic energy gains. Two idealisations are built into the question and are worth naming: air resistance is being ignored, and g does in fact shrink very slightly with height, but over the few metres of a drop onto a floor the change is far too small to matter.
- (b)Its momentum — Momentum is mass times velocity. The mass is fixed but the velocity keeps growing at 9.8 metres per second every second, so momentum grows in step with it — indeed the rate at which momentum changes is what the weight force is.
- (c)Its kinetic energy — Kinetic energy is half the mass times the square of the speed, and the speed is rising throughout the fall. It starts at zero for an object simply released and is largest at the instant before impact.
- (d)Its potential energy — Gravitational potential energy is mass times g times height, and the height is falling. The potential energy therefore falls continuously, and the amount lost equals the kinetic energy gained — which is the very statement that the total energy, and not the potential energy, is what is conserved.
Free fall is the standard first illustration of Newton's second law. The gravitational force on a body of mass m near the Earth is mg, so its acceleration is mg divided by m, which is g regardless of how heavy the body is. This is why a stone and a feather fall together in a vacuum. A constant acceleration is what makes the equations of uniformly accelerated motion apply — the speed after falling through a height h is the square root of twice g times h, and that is the speed at which the object meets the floor.
Read the stem's word uniform as unchanging with time, not as identical for all objects. Three of the four options are quantities that depend on the speed or the height, both of which are changing every instant, so they can be struck out without any calculation. That leaves acceleration, and the reason it is constant is that the force producing it is constant. A useful cross-check comes from energy: potential energy falls, kinetic energy rises, and their sum stays put — so if the question had offered total mechanical energy as an option, that would also have been uniform.
- In free fall the only force is weight, so the acceleration is g and is independent of the mass.
- Near the Earth's surface g is about 9.8 metres per second squared.
- Speed after falling a height h is the square root of 2gh, so the speed and the momentum both grow during the fall.
- Kinetic energy grows as the square of the speed while potential energy falls by an equal amount.
- The question assumes no air resistance, and treats g as constant over the height of the drop.
The force is constant, so the acceleration is constant — everything that depends on speed or height is not.
- Reading uniform as the same for all bodies rather than as constant in time.
- Choosing potential energy because it changes in a simple straight-line way; simple change is still change.
- Forgetting that the question quietly assumes no air resistance.
As a which-quantity-stays-constant item like this one, or as a short numerical asking for the speed or the energy with which the body strikes the ground.
A rigid body of mass 2 kg is dropped from a stationary balloon kept at a height of 50 m from the ground. The speed of the body when it just touches the ground and the total energy when it is dropped from the balloon are respectively (acceleration due to gravity = 9·8 m/s²)
- (a) 980 m s⁻¹ and 980 J
- (b) √980 m s⁻¹ and √980 J
- (c) 980 m s⁻¹ and √980 J
- (d) √980 m s⁻¹ and 980 J
Answer(d) √980 m s⁻¹ and 980 J
The same fall, worked out with numbers. Constant acceleration is what lets the speed at the ground be found from the square root of 2gh, and the total energy of 980 joules stays put throughout the drop even as it changes from potential to kinetic.
- practice — not a real PYQ
A stone is released from rest and falls freely. Ignoring air resistance, which one of the following grows as the square of the time elapsed?
- (a)Its acceleration
- (b)Its speed
- (c)The distance it has fallen
- (d)Its mass
Answer(c) The distance it has fallen — for a start from rest the distance is half of g times the square of the time, while the speed grows only in proportion to time.
- practice — not a real PYQ
A body is dropped from a height of 20 m. Taking g as 10 m/s² and ignoring air resistance, its speed on reaching the ground is
- (a)10 m/s
- (b)20 m/s
- (c)40 m/s
- (d)200 m/s
Answer(b) 20 m/s — the speed is the square root of 2gh, which is the square root of 400.