Select the best answer for the question. Which statement accurately describes the relationship between mass and weight?
A. An object with twice the mass of another object will weigh four times as much.
B. An object with twice the mass of another object will weigh twice as much.
C. An object with twice the mass of another object will weigh half as much.
D. An object with twice the mass of another object will weigh one-fourth as much.
Answer (2)
Weight is directly proportional to mass, as described by the formula W = m g . An object with twice the mass of another will weigh twice as much, making Option B the correct answer. Thus, the statement "An object with twice the mass of another object will weigh twice as much" accurately reflects this relationship.
;
Weight is directly proportional to mass, described by the formula W = m g .
If the mass doubles ( m 2 = 2 m 1 ), the weight also doubles ( W 2 = 2 W 1 ).
Therefore, an object with twice the mass weighs twice as much.
The correct answer is B: An object with twice the mass of another object will weigh twice as much. B
Explanation
Understanding the Problem The question asks us to identify the correct relationship between an object's mass and its weight. We need to consider how weight changes when mass is altered.
Recalling the Formula Weight is the force exerted on an object due to gravity. The relationship between mass and weight is given by the formula: W = m g where:
W is the weight of the object,
m is the mass of the object, and
g is the acceleration due to gravity (approximately 9.8 m / s 2 on Earth, and it is constant for a given location).
Calculating the New Weight Let's say we have an object with mass m 1 and weight W 1 . Then, W 1 = m 1 g Now, consider another object with twice the mass, so m 2 = 2 m 1 . Its weight W 2 will be: W 2 = m 2 g = ( 2 m 1 ) g = 2 ( m 1 g ) = 2 W 1 This shows that if an object has twice the mass, its weight will be twice as much.
Selecting the Correct Option Comparing our result with the given options:
Option A states: An object with twice the mass of another object will weigh four times as much. (Incorrect)
Option B states: An object with twice the mass of another object will weigh twice as much. (Correct)
Option C states: An object with twice the mass of another object will weigh half as much. (Incorrect)
Option D states: An object with twice the mass of another object will weigh one-fourth as much. (Incorrect) Therefore, the correct answer is option B.
Final Answer The correct statement is that an object with twice the mass of another object will weigh twice as much.
Examples
Imagine you're lifting weights at the gym. If you double the amount of weight (mass) you're lifting, you'll feel twice the force (weight) because weight is directly proportional to mass. This concept is also crucial in engineering, where calculating the weight of materials based on their mass is essential for designing safe and stable structures, like bridges and buildings. Understanding the relationship between mass and weight helps ensure that structures can withstand the forces acting upon them.
