Which statement accurately describes the relationship between mass and weight?
A) An object with twice the mass of another object will weigh half as much.
B) An object with twice the mass of another object will weigh one-fourth as much.
C) An object with twice the mass of another object will weigh four times as much.
D) An object with twice the mass of another object will weigh twice as much.
Answer (1)
Weight is directly proportional to mass, described by the formula W = m g .
If mass doubles, weight also doubles.
Options A, B, and C are incorrect because they do not reflect this direct proportionality.
Option D accurately describes the relationship: an object with twice the mass weighs twice as much. D
Explanation
Understanding the Problem The question asks us to identify the correct relationship between an object's mass and its weight. We are given four options, each describing how the weight changes when the mass is doubled.
Recalling the Formula Weight is the force exerted on an object due to gravity. The relationship between mass ( m ) and weight ( W ) is given by the formula: W = m g where g is the acceleration due to gravity (approximately 9.8 m / s 2 on Earth). This formula tells us that weight is directly proportional to mass.
Analyzing the Options Let's analyze each option:
A) If an object has twice the mass, its weight will be twice as much, not half. So, option A is incorrect.
B) If an object has twice the mass, its weight will be twice as much, not one-fourth. So, option B is incorrect.
C) If an object has twice the mass, its weight will be twice as much, not four times. So, option C is incorrect.
D) If an object has twice the mass, its weight will be twice as much. This aligns with the formula W = m g . So, option D is correct.
Conclusion Therefore, the correct statement is that an object with twice the mass of another object will weigh twice as much.
Examples
Imagine you're comparing two bags of groceries. If one bag has twice the mass of the other, it will also 'weigh' twice as much on a scale because weight is directly proportional to mass. This concept is crucial in fields like physics and engineering, where understanding the relationship between mass and weight is essential for designing structures, calculating forces, and ensuring stability. For example, engineers must consider the weight of materials when designing bridges to ensure they can withstand the gravitational forces acting upon them. This ensures safety and prevents structural failure.
