Which of the following measurements depends on the value of the local gravitational field and therefore can change from place to place?

Introduction / Context:
In mechanics, it is important to distinguish between mass and weight. Mass is an intrinsic property of matter, while weight is the gravitational force acting on that mass. This distinction explains why an object would "weigh" less on the Moon even though the amount of matter in it does not change. This question asks which measurement depends directly on the gravitational field strength and can vary from place to place.

Given Data / Assumptions:

• Mass is the amount of matter in a body.
• Weight is the force due to gravity acting on that mass.
• Height is a geometric length measured along the vertical direction.
• Gravitational acceleration g can vary between planets and slightly on Earth.

Concept / Approach:
The weight W of a body is given by W = m * g, where m is mass and g is the local acceleration due to gravity. Mass does not depend on g and remains the same whether the object is on Earth, the Moon, or in space. Height is a length measurement and is not directly determined by gravitational acceleration, although gravity influences growth and structures in broader ways. Since weight is directly proportional to g, any change in g leads to a change in weight, making weight the measurement that depends on the local gravitational field.

Step-by-Step Solution:
Step 1: Write the formula for weight: W = m * g. Step 2: Note that mass m is an intrinsic property of the body and does not change with location. Step 3: Recognise that g is different on Earth, Moon, and other planets. For example, g on the Moon is about one sixth of that on Earth. Step 4: Since W depends on g, the same body has different weights at locations with different gravitational acceleration. Step 5: Height is measured as a length and does not have g in its definition, so it is not directly dependent on gravitational field strength.

Verification / Alternative check:
A person who has a weight of 600 newton on Earth will have a weight of about 100 newton on the Moon if mass is constant. Bathroom scales measure weight and give different readings when g changes. However, if you measure the mass of the same object using a balance that compares it with standard masses, the mass will be found unchanged. This practical observation confirms that weight depends on g, not mass or pure length.

Why Other Options Are Wrong:
Mass: It is independent of the gravitational field and remains constant for a body everywhere. Height: It is a measure of length and does not involve g in its basic definition. All of the above: This is incorrect because only weight directly depends on g among the listed quantities.

Common Pitfalls:
A frequent mistake is to use the words mass and weight interchangeably in daily language, which leads to confusion in physics. Another misconception is to think that a body "loses mass" on the Moon because the weighing scale reading changes. To avoid this, remember that mass measures quantity of matter, while weight measures gravitational force, and only weight involves the factor g explicitly.

Final Answer:
The measurement that depends on the value of the local gravitational field is weight.