Understanding Free Fall for Objects with Different Masses

The question asks about two balls of the same diameter but different masses (2.5 kg iron ball and 1.25 kg aluminium ball) being dropped simultaneously from a cliff. We need to determine which physical quantity is the same for both balls just before they reach the ground, assuming air resistance is negligible.

Analyzing Acceleration in Free Fall

In the realm of physics, specifically when discussing motion under gravity, the concept of free fall is crucial. Free fall is defined as the motion of an object where the only force acting upon it is gravity. A fundamental principle of physics, demonstrated famously by Galileo Galilei, is that in the absence of air resistance, all objects in free fall accelerate downwards at the same rate, regardless of their mass or composition. This acceleration is known as the acceleration due to gravity.

The acceleration due to gravity, denoted by 'g', is approximately $9.8 \, \text{m/s}^2$ near the Earth's surface. It is the same for the 2.5 kg iron ball and the 1.25 kg aluminium ball when they are dropped from the same height from a cliff, assuming we ignore air resistance. Since they are dropped at the same time and experience the same constant acceleration, their velocities will also be the same at any given point in their descent, including just before they reach the ground.

Therefore, the acceleration of both balls is the same throughout their free fall, and specifically, just before they reach the ground. This is a key concept when studying the motion of objects with different masses under gravity.

Comparing Other Quantities

Let's consider the other options provided and see if they would be the same for both balls just before they reach the ground after being dropped from a cliff.

• Momentum: Momentum (p) is calculated as the product of mass (m) and velocity (v), i.e., $p = mv$. While the velocity (v) just before reaching the ground is the same for both balls (as they had the same acceleration and fell for the same time), their masses (m) are different (2.5 kg vs 1.25 kg). Thus, their momentum will be different. The iron ball, having greater mass, will have greater momentum.
• Kinetic Energy: Kinetic energy (KE) is calculated as $\text{KE} = \frac{1}{2}mv^2$. Again, the velocity (v) is the same for both balls just before reaching the ground. However, their masses (m) are different. The kinetic energy depends on mass, so the kinetic energy of the iron ball will be greater than that of the aluminium ball. This is another example of how different masses lead to different outcomes for quantities dependent on mass during free fall.
• Potential Energy: Potential energy (PE) relative to the ground is calculated as $\text{PE} = mgh$, where m is mass, g is acceleration due to gravity, and h is height. The height just before reaching the ground is effectively zero relative to the ground for both balls. Therefore, their potential energy relative to the ground at this instant is zero. While zero is the same value, the question is typically asking about a property characteristic of their state or motion *derived from* the fall itself. More importantly, their *initial* potential energies from the cliff were different due to their different masses. The energy transformation during the motion involves initial potential energy converting to kinetic energy.

Based on the principles of physics governing motion under gravity, the only quantity among the options that is the same for objects of different masses in free fall (neglecting air resistance) is their acceleration.

Therefore, just before they reach the ground, the iron ball and the aluminium ball have the same acceleration, which is the acceleration due to gravity.