Consider the given statement to be true and decide which of the conclusion(s) logically follow(s) from the statement. Statement: Weight is also a force. Conclusions:
1. The unit of weight is Newton.
2. The unit of weight is Kilogram.
Only conclusion 1 follows.
Understanding Weight and Force: Logical Conclusions
The question asks us to consider a given statement as true and determine which of the provided conclusions logically follow from it. The statement is: Weight is also a force.
We are given two conclusions about the unit of weight:
- The unit of weight is Newton.
- The unit of weight is Kilogram.
We need to analyze each conclusion based on the truth of the statement that weight is a force.
Analyzing Conclusion 1: Unit of Weight is Newton
The statement says that weight is a force. In physics, forces are typically measured in the unit called Newton (N). This unit is part of the International System of Units (SI). Examples of forces include applied force, friction, tension, and gravity. The force due to gravity acting on an object with mass is what we call weight.
Since the statement establishes a direct relationship, stating weight is a force, it implies that weight shares fundamental characteristics with other forces, including its standard unit of measurement.
Therefore, if weight is a force, its unit should logically be the unit of force, which is Newton. Conclusion 1 seems to follow directly from the premise.
Analyzing Conclusion 2: Unit of Weight is Kilogram
Conclusion 2 states that the unit of weight is Kilogram (kg). Kilogram is the standard SI unit for measuring mass. Mass is a measure of the amount of matter in an object and its resistance to acceleration (inertia). Weight, on the other hand, is the gravitational force acting on an object's mass.
The relationship between weight ($W$) and mass ($m$) is given by the formula:
\(W = m \times g\)
where \(g\) is the acceleration due to gravity (approximately \(9.8 \, m/s^2\) on Earth).
Looking at the units:
- The unit of mass ($m$) is Kilogram (kg).
- The unit of acceleration ($g$) is meters per second squared (\(m/s^2\)).
- Therefore, the unit of weight ($W$) is \(kg \times m/s^2\).
One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared (\(1 \, N = 1 \, kg \cdot m/s^2\)).
Thus, the unit \(kg \cdot m/s^2\) is equivalent to the Newton (N). This confirms that the unit of weight is indeed Newton, not Kilogram.
While weight is related to mass, they are different physical quantities with different units. The statement explicitly equates weight to force, not mass. Therefore, stating that the unit of weight is Kilogram does not logically follow from the statement that weight is a force.
Evaluating the Conclusions
- Conclusion 1: "The unit of weight is Newton." This logically follows from the statement "Weight is also a force," because Newton is the standard unit for force.
- Conclusion 2: "The unit of weight is Kilogram." This does not logically follow from the statement "Weight is also a force," because Kilogram is the unit of mass, not force.
Based on the logical deductions from the given statement, only conclusion 1 follows.
Revision Table: Weight vs. Mass Units
| Concept | Definition | Standard SI Unit |
|---|---|---|
| Mass | Amount of matter; measure of inertia | Kilogram (kg) |
| Weight | Gravitational force on an object's mass | Newton (N) |
| Force | Interaction causing change in motion | Newton (N) |
Additional Information on Weight and Force
It's a common point of confusion, but mass and weight are distinct concepts. Mass is an intrinsic property of an object that remains the same regardless of location (unless matter is added or removed). Weight, however, is the force of gravity acting on the mass. It changes depending on the gravitational acceleration, which varies slightly at different points on Earth and significantly on other celestial bodies.
For example, an astronaut's mass is the same on the Moon as on Earth, but their weight on the Moon is much less because the Moon's gravity is weaker than Earth's. The statement in the question clarifies this by classifying weight as a force, emphasizing its nature as a gravitational pull measured in units appropriate for forces (Newtons), rather than units for mass (Kilograms).
Similar Questions
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Important Questions from Statements and Conclusions
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I. Some A are C.
II. Some A are not C.
III. Some A are B.
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Statement:
A asked C, "What time is it now?" Is it half past two? ''
Conclusions:
1. A wants to go to lunch.
2. A wants to confirm what the time is because his watch is off.
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