To determine how an object's weight changes from Earth to the Moon, we need to understand the definition of weight and the factors influencing it, particularly gravitational acceleration. Weight is the force exerted on an object due to gravity, and it depends on both the object's mass and the gravitational acceleration of the celestial body it is on.
Correct Option: B) It decreases
This question asks for the fundamental relationship between weight, mass, and gravitational acceleration. This is a core concept in physics, specifically Newton's second law of motion applied to gravity.
B) \(W = m \times g\) — This equation correctly represents weight as the product of mass and gravitational acceleration, which is a direct application of Newton's second law of motion where gravitational force is the acting force.
The question asks to differentiate between weight and mass. We need to understand the fundamental definitions and characteristics of both physical quantities to identify the correct statement.
A) Weight depends on the gravitational force acting on an object, while mass is a measure of the amount of matter in an object. This option correctly distinguishes between weight and mass based on their definitions and dependencies. Mass is an intrinsic property, a measure of inertia, and the amount of matter. Weight is the force of gravity acting on that mass, and thus it varies with the gravitational field.
The question asks about the relationship between weight and altitude. Weight is a measure of the gravitational force acting on an object, which depends on its mass and the acceleration due to gravity. We need to understand how the acceleration due to gravity changes with altitude.
B) Weight decreases with altitude. As shown in the step-by-step explanation, the acceleration due to gravity, and consequently the weight of an object, decreases as its distance from the Earth's center (i.e., altitude) increases.
Which of the following is a unit of weight in the FPS system?
The question asks to identify a unit of weight in the FPS (Foot-Pound-Second) system. To answer this, we need to recall the fundamental units of mass, length, and time in different systems of measurement, specifically focusing on the FPS system and distinguishing between mass and weight units.
C) Pound is a unit of weight (specifically, pound-force) in the FPS system. It represents the force exerted by gravity on a pound of mass. While 'pound' can also refer to pound-mass, in the context of weight, it implies pound-force in the FPS system.
To determine how weight changes on the Moon compared to Earth, we need to understand the definition of weight and the factors that influence it, primarily gravity. Weight is the force exerted on an object due to gravity, and it depends on the mass of the object and the acceleration due to gravity of the celestial body.
Define Weight: Weight (\(W\)) is the force of gravity acting on an object's mass (\(m\)). It is given by the formula:
\[ W = m \times g \]where \(g\) is the acceleration due to gravity.
Mass vs. Weight: It's crucial to distinguish between mass and weight. Mass is a measure of the amount of matter in an object and remains constant regardless of location. Weight, however, is a force and varies depending on the gravitational field.
Gravitational Acceleration on Earth (\(g_E\)): On Earth, the average acceleration due to gravity is approximately \(9.8 \, \text{m/s}^2\).
Gravitational Acceleration on the Moon (\(g_M\)): The Moon has significantly less mass and a smaller radius than Earth. As a result, its gravitational pull is much weaker. The acceleration due to gravity on the Moon is approximately one-sixth of that on Earth:
\[ g_M \approx \frac{1}{6} g_E \]Compare Weight: Since mass (\(m\)) remains constant, the weight of an object on the Moon (\(W_M\)) will be:
\[ W_M = m \times g_M = m \times \left(\frac{1}{6} g_E\right) = \frac{1}{6} (m \times g_E) = \frac{1}{6} W_E \]This means an object's weight on the Moon is approximately one-sixth of its weight on Earth.
Correct Option: B) Weight on the Moon is lesser than on Earth.
As derived, the acceleration due to gravity on the Moon is about one-sixth of that on Earth. Since weight is directly proportional to the acceleration due to gravity, an object will weigh less on the Moon than on Earth.