In classical mechanics, the law of falling bodies stated by Galileo is commonly known by which other descriptive name?

Introduction / Context:
Before Newton formalised the laws of motion and universal gravitation, Galileo carried out systematic experiments on falling objects. His work on falling bodies overturned the old Aristotelian idea that heavier objects fall faster than lighter ones. Galileo showed that, in the absence of air resistance, all bodies near the surface of the Earth fall with the same constant acceleration. This result is often referred to as Galileos law of falling bodies. The question asks you to identify another descriptive name used for this same idea in basic mechanics textbooks.

Given Data / Assumptions:
• We are dealing with motion of bodies falling freely under gravity near the Earth surface. • Air resistance and other resistive forces are neglected. • The law attributed to Galileo states that all freely falling bodies have the same constant acceleration. • The options list several well known laws and principles from mechanics.

Concept / Approach:
Galileos experiments showed that in uniform gravitational fields, the acceleration of a freely falling body is constant and independent of its mass. This result implies that the displacement of a falling body is proportional to the square of the time of fall when starting from rest. Because the acceleration is constant, the motion is described as uniformly accelerated motion. Therefore, Galileos law of falling bodies is commonly described as the law of uniform acceleration of freely falling bodies. This descriptive name captures the key content of his law without using more modern Newtonian terminology.

Step-by-Step Solution:
Step 1: Recall that Galileo emphasised experimental observation of bodies falling from towers and sliding on inclined planes. Step 2: From these experiments, he concluded that all objects in free fall (ignoring air resistance) accelerate at the same constant rate. Step 3: Constant acceleration is referred to in mechanics as uniform acceleration. Step 4: Combine these ideas to obtain a descriptive title: law of uniform acceleration of freely falling bodies. Step 5: Compare this descriptive name with the options given in the question. Step 6: Select the option that exactly mentions uniform acceleration of freely falling bodies as the alternative name.

Verification / Alternative check:
Looking at introductory physics textbooks, the equations of motion for bodies under constant acceleration due to gravity are often derived in the context of Galileos findings. Relationships such as s = (1/2) * g * t^2 and v = g * t for a body starting from rest are direct consequences of uniform acceleration. Historical notes frequently credit Galileo with discovering that the acceleration of falling bodies is constant and independent of mass. This confirms that the phrase law of uniform acceleration of freely falling bodies accurately reflects the content of his law of falling bodies.

Why Other Options Are Wrong:
Option B, law of inertia of motion, is more closely associated with Newtons first law, which states that a body remains at rest or moves with constant velocity unless acted on by a net external force. It does not emphasise uniform acceleration under gravity. Option C, law of universal gravitation, is Newtons formulation describing the gravitational attraction between masses and is different in form and scope from Galileos simple falling body law. Option D, law of conservation of momentum, relates to interactions and collisions between bodies, not to the uniform acceleration of a single falling object. None of these alternatives captures Galileos specific result about uniform acceleration in free fall.

Common Pitfalls:
A common mistake is to assume that all classical mechanics laws must be one of Newtons three laws or his law of gravitation, and to ignore earlier contributions. This can lead students to incorrectly associate Galileos work directly with Newtons named laws. Another pitfall is not recognising that the phrase uniform acceleration directly connects to the constant acceleration due to gravity, g, near the Earth surface. Keeping track of which law deals with which physical situation helps you match historical names and descriptive titles correctly in exam questions.

Final Answer:
The correct choice is Law of uniform acceleration of freely falling bodies, because Galileos law of falling bodies states that all freely falling objects near the Earth surface experience the same constant acceleration, which is uniform acceleration under gravity.