Which one of the following statements for an object falling freely under the influence of gravity is correct?
- (a)Zero acceleration always implies zero velocity
- (b)Zero acceleration has no relation with the velocity of the object
- (c)Zero velocity at any instant necessarily means zero acceleration at that instant
- (d)Acceleration is constant all throughout the free fall
Correct — D, Acceleration is constant all throughout the free fall. Free fall means gravity is the only force acting. Newton's second law then gives a = mg/m = g, and the mass cancels out, so every falling body near the Earth's surface picks up speed at the same fixed rate of about 9.8 metres per second every second. The velocity changes from moment to moment; the acceleration producing that change does not.
- (a)Zero acceleration always implies zero velocity — A body moving at a steady 60 km/h has zero acceleration and a very large velocity. Zero acceleration says the velocity is not changing, not that it is nothing.
- (b)Zero acceleration has no relation with the velocity of the object — Zero acceleration is a statement about velocity — it says velocity stays constant. Calling the two unrelated goes too far in the opposite direction from option (a).
- (c)Zero velocity at any instant necessarily means zero acceleration at that instant — Throw a stone straight up and at the highest point its velocity passes through zero, yet gravity is still pulling it down at 9.8 m/s². That single instant is the counter-example the examiner has in mind.
Velocity and acceleration are separate quantities, and at any given instant the value of one places no restriction on the value of the other. Velocity is how fast the position is changing; acceleration is how fast the velocity is changing. A body can have large velocity with zero acceleration, zero velocity with large acceleration, or any other combination.
Free fall in physics has a strict meaning — gravity acts and nothing else, so no air resistance. Under that condition the accelerating force is mg and the resisting inertia is m, and the two cancel, which is why a hammer and a feather dropped together on the airless Moon landed together in the Apollo 15 demonstration. Once air is allowed back in, drag grows with speed until it balances the weight and the acceleration drops to zero at terminal velocity, which is why a parachutist eventually stops speeding up. The question rules that case out by saying free fall.
- Free fall means gravity is the only force acting; the acceleration is g, about 9.8 m/s² near the Earth's surface.
- The acceleration in free fall does not depend on the mass, the shape or the speed already gained.
- At the top of a vertical throw the velocity is momentarily zero while the acceleration is still g downwards.
- g is not quite uniform over the Earth — roughly 9.78 m/s² at the equator against 9.83 m/s² at the poles, because the Earth bulges at the equator.
- With air resistance included the fall is no longer free: drag rises with speed until the net force vanishes and the body settles at terminal velocity.
Only the middle row is unusual, and it is the row that kills option (c). The right-hand column never changes, which is the whole content of option (d).
- Treating 'at rest for an instant' as 'not accelerating'.
- Believing a heavier body falls faster, which is true only when air resistance is in play.
- Forgetting that acceleration keeps pointing downward even while the body is travelling upward.
A statement-picking item on the definition of free fall, where three options attack the same confusion between velocity and acceleration from three angles.
The free fall acceleration g increases as one proceeds, at sea level, from the equator toward either pole. The reason is
- (a) Earth is a sphere with same density everywhere
- (b) Earth is a sphere with different density at the polar regions than in the equatorial regions
- (c) Earth is approximately an ellipsoid having its equatorial radius greater than its polar radius by 21 km
- (d) Earth is approximately an ellipsoid having its equatorial radius smaller than its polar radius by 21 km
Answer(c) Earth is approximately an ellipsoid having its equatorial radius greater than its polar radius by 21 km
The one qualification worth carrying alongside 'g is constant'. It is constant through any single fall, but its value at the poles is slightly larger than at the equator because the poles sit closer to the Earth's centre.
Which one of the following holds true for a freely falling object?
- (a) It moves with a uniform velocity.
- (b) It moves with a uniform speed.
- (c) It moves with a non-uniform acceleration.
- (d) It moves with a uniform acceleration.
Answer(d) It moves with a uniform acceleration.
CAPF asked the identical fact three years later, stripped of the disguise. Uniform acceleration with a steadily changing speed is precisely what makes options (a) and (b) there, and option (c) here, wrong.
- practice — not a real PYQ
A ball is thrown vertically upward. At the instant it reaches its maximum height, which one of the following is correct?
- (a)Both velocity and acceleration are zero
- (b)Velocity is zero and acceleration is 9.8 m/s² downward
- (c)Velocity is 9.8 m/s and acceleration is zero
- (d)Both velocity and acceleration point upward
Answer(b) Velocity is zero and acceleration is 9.8 m/s² downward — gravity never switches off, so the ball is at rest for only one instant before falling back.
- practice — not a real PYQ
Two stones of mass 1 kg and 5 kg are released together from the same height in a vacuum. Which one of the following is correct?
- (a)The 5 kg stone lands first
- (b)The 1 kg stone lands first
- (c)Both land together
- (d)It depends on their shapes
Answer(c) Both land together — the accelerating force mg and the inertia m grow in step, so the acceleration is g for both and shape matters only when air is present.