The question asks to identify the true statement about weight. To answer this, we need to understand the definition of weight, its properties, and how it differs from mass.
C) Weight is a vector quantity. Weight is a force, and all forces are vector quantities, meaning they have both magnitude and direction (towards the center of the gravitational body).
To determine which factor affects the weight of an object, we need to understand the definition of weight and its relationship with other physical quantities. Weight is a measure of the gravitational force exerted on an object.
A) Mass. The weight of an object is directly proportional to its mass, as given by the formula \(W = m \times g\). Therefore, mass is a fundamental factor affecting an object's weight.
The question asks to identify the true statement among the given options regarding weight and mass. To answer this, we need to understand the fundamental definitions and properties of mass and weight.
Upon re-examination of the provided options and the designated correct answer B, there seems to be a discrepancy. The statement in option B, "Weight is the same everywhere in the universe, while mass varies," is physically incorrect. Mass is constant, and weight varies. If the question intended to state the opposite for option B (i.e., "Mass is the same everywhere in the universe, while weight varies\
The question asks to identify the law that establishes a direct proportionality between an object's weight and its mass. We need to recall the fundamental laws of physics, particularly Newton's laws of motion and the law of universal gravitation, and their mathematical formulations.
B) Newton's Second Law — Newton's Second Law, \(F = m \cdot a\), directly leads to the definition of weight as \(W = m \cdot g\), where \(W\) is the force (weight) and \(g\) is the acceleration due to gravity. This equation clearly demonstrates that weight is directly proportional to mass.
To determine what happens to an object's weight on the Moon, we need to understand the definition of weight and how it differs from mass. Weight is a measure of the gravitational force acting on an object, which depends on both the object's mass and the gravitational acceleration of the celestial body it is on.
Mass (\(m\)): This is an intrinsic property of an object, representing the amount of matter it contains. Mass remains constant regardless of location (unless matter is added or removed).
Weight (\(W\)): This is the force of gravity acting on an object's mass. It is calculated using the formula:
\[ W = m \times g \]where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity.
The acceleration due to gravity (\(g\)) varies from one celestial body to another. The Earth's gravitational acceleration is approximately \(g_{\text{Earth}} = 9.8 \, \text{m/s}^2\).
The Moon's gravitational acceleration is significantly less than Earth's, approximately \(g_{\text{Moon}} \approx 1.62 \, \text{m/s}^2\), which is about one-sixth of Earth's gravity.
Since the mass (\(m\)) of the object remains constant, but the acceleration due to gravity (\(g\)) on the Moon is less than on Earth, the weight of the object on the Moon will be less than its weight on Earth.
\[ W_{\text{Moon}} = m \times g_{\text{Moon}} \]\[ W_{\text{Earth}} = m \times g_{\text{Earth}} \]Since \(g_{\text{Moon}} < g_{\text{Earth}}\), it follows that \(W_{\text{Moon}} < W_{\text{Earth}}\).
B) It decreases
The weight of an object is directly proportional to the acceleration due to gravity. Since the Moon's gravitational acceleration is about one-sixth that of Earth's, an object's weight on the Moon will be approximately one-sixth of its weight on Earth, meaning it decreases.