Question
John releases various objects from an identical height on Earth. The provided table displays his collected data.
Object | Mass (kg) | Gravitational Force on the Object (N)
1 | 1 | 9.8
2 | 10 | 98
3 | 100 | 980
4 | 1,000 | 9800
A. The gravitational force acting on an object is equal to one-tenth of its mass.
B. Objects with greater mass experience a reduced gravitational force.
C. Objects with a higher mass experience a greater gravitational force acting upon them.
D. The gravitational force acting on an object is tenfold higher than its mass.
Object | Mass (kg) | Gravitational Force on the Object (N)
1 | 1 | 9.8
2 | 10 | 98
3 | 100 | 980
4 | 1,000 | 9800
A. The gravitational force acting on an object is equal to one-tenth of its mass.
B. Objects with greater mass experience a reduced gravitational force.
C. Objects with a higher mass experience a greater gravitational force acting upon them.
D. The gravitational force acting on an object is tenfold higher than its mass.
Answers
GPT-4o mini
To analyze the provided statements, let's first recall the relationship between gravitational force (F), mass (m), and acceleration due to gravity (g), which is expressed as:
\[ F = m \times g \]
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \).
Now, let's assess the provided statements based on the data:
A. **The gravitational force acting on an object is equal to one-tenth of its mass.**
- This statement is incorrect. The gravitational force acting on an object is not one-tenth of its mass; rather, it is proportional to the mass multiplied by the acceleration due to gravity.
B. **Objects with greater mass experience a reduced gravitational force.**
- This statement is incorrect. The gravitational force acting on an object increases with greater mass; it is not reduced.
C. **Objects with a higher mass experience a greater gravitational force acting upon them.**
- This statement is correct. As shown in the data, the gravitational force increases with the mass of the objects.
D. **The gravitational force acting on an object is tenfold higher than its mass.**
- This statement is partially misleading. The gravitational force is actually \( 9.8 \times m \), which is roughly tenfold (around \( 9.8 \) times the mass in kg). However, saying "tenfold" can create confusion because it's not exactly ten times; it's slightly less.
In summary:
- Statement C is definitely correct.
- Statements A and B are incorrect.
- Statement D is somewhat true but should be stated with caution regarding the precision of "tenfold."
Thus, the most accurate conclusion is:
**C. Objects with a higher mass experience a greater gravitational force acting upon them.**
\[ F = m \times g \]
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \).
Now, let's assess the provided statements based on the data:
A. **The gravitational force acting on an object is equal to one-tenth of its mass.**
- This statement is incorrect. The gravitational force acting on an object is not one-tenth of its mass; rather, it is proportional to the mass multiplied by the acceleration due to gravity.
B. **Objects with greater mass experience a reduced gravitational force.**
- This statement is incorrect. The gravitational force acting on an object increases with greater mass; it is not reduced.
C. **Objects with a higher mass experience a greater gravitational force acting upon them.**
- This statement is correct. As shown in the data, the gravitational force increases with the mass of the objects.
D. **The gravitational force acting on an object is tenfold higher than its mass.**
- This statement is partially misleading. The gravitational force is actually \( 9.8 \times m \), which is roughly tenfold (around \( 9.8 \) times the mass in kg). However, saying "tenfold" can create confusion because it's not exactly ten times; it's slightly less.
In summary:
- Statement C is definitely correct.
- Statements A and B are incorrect.
- Statement D is somewhat true but should be stated with caution regarding the precision of "tenfold."
Thus, the most accurate conclusion is:
**C. Objects with a higher mass experience a greater gravitational force acting upon them.**