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 twice 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 one-fourth as much.
Answer (1)
Weight is directly proportional to mass: W e i g h t = ma ss × g r a v i t a t i o na l a cce l er a t i o n .
If mass doubles, weight also doubles.
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 Mass and Weight Let's analyze the relationship between mass and weight. Mass is the amount of matter in an object, while weight is the force of gravity acting on that mass. The formula that connects these two is:
The Formula W e i g h t = ma ss × g r a v i t a t i o na l a cce l er a t i o n
Direct Proportionality This formula tells us that weight is directly proportional to mass. If we double the mass, we double the weight, assuming the gravitational acceleration remains constant.
Comparing Two Objects Let's consider two objects. Object 1 has mass m 1 and weight w 1 . Object 2 has mass m 2 and weight w 2 . We are given that m 2 = 2 × m 1 . We want to find the relationship between w 1 and w 2 .
Calculating the Relationship We know that: w 1 = m 1 × g w 2 = m 2 × g Since m 2 = 2 × m 1 , we can substitute this into the second equation: w 2 = ( 2 × m 1 ) × g = 2 × ( m 1 × g ) = 2 × w 1 So, w 2 = 2 × w 1 . This means that object 2 weighs twice as much as object 1.
Conclusion Therefore, the correct statement is: An object with twice the mass of another object will weigh twice as much.
Examples
Understanding the relationship between mass and weight is crucial in many real-world scenarios. For example, when designing bridges or buildings, engineers need to consider the weight of the materials they are using. If they double the amount of material (and thus double the mass), they need to account for the fact that the weight will also double. This relationship is also important in fields like aerospace engineering, where the weight of a spacecraft is a critical factor in determining how much fuel is needed for a mission. By understanding the direct proportionality between mass and weight, engineers can make accurate calculations and ensure the safety and efficiency of their designs.
