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What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved?
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What will be the gravitational force if the mass of one of the object ...
Understanding Gravitational Force
The gravitational force between two objects is calculated using Newton's law of universal gravitation, which is expressed as:
\[ F = G \frac{{m_1 \cdot m_2}}{{r^2}} \]
where:
- \( F \) = gravitational force
- \( G \) = gravitational constant
- \( m_1 \) and \( m_2 \) = masses of the two objects
- \( r \) = separation between the centers of the two objects
Scenario Change: Doubling Mass and Halving Distance
1. **Doubling the Mass**
If we double the mass of one object (let's say \( m_1 \) becomes \( 2m_1 \)):
- New force \( F' = G \frac{{(2m_1) \cdot m_2}}{{r^2}} = 2 \cdot G \frac{{m_1 \cdot m_2}}{{r^2}} = 2F \)
2. **Halving the Distance**
If we halve the separation between the two objects (let's say \( r \) becomes \( \frac{r}{2} \)):
- New force \( F'' = G \frac{{m_1 \cdot m_2}}{{(\frac{r}{2})^2}} = G \frac{{m_1 \cdot m_2}}{{\frac{r^2}{4}}} = 4G \frac{{m_1 \cdot m_2}}{{r^2}} = 4F \)
Final Calculation of Gravitational Force
When both changes occur simultaneously:
- The new gravitational force \( F_{new} \) becomes:
\[ F_{new} = 2F \times 4 = 8F \]
Thus, the gravitational force will increase by a factor of **8** if the mass of one object is doubled and the separation between the two objects is halved.
The gravitational force between two objects is calculated using Newton's law of universal gravitation, which is expressed as:
\[ F = G \frac{{m_1 \cdot m_2}}{{r^2}} \]
where:
- \( F \) = gravitational force
- \( G \) = gravitational constant
- \( m_1 \) and \( m_2 \) = masses of the two objects
- \( r \) = separation between the centers of the two objects
Scenario Change: Doubling Mass and Halving Distance
1. **Doubling the Mass**
If we double the mass of one object (let's say \( m_1 \) becomes \( 2m_1 \)):
- New force \( F' = G \frac{{(2m_1) \cdot m_2}}{{r^2}} = 2 \cdot G \frac{{m_1 \cdot m_2}}{{r^2}} = 2F \)
2. **Halving the Distance**
If we halve the separation between the two objects (let's say \( r \) becomes \( \frac{r}{2} \)):
- New force \( F'' = G \frac{{m_1 \cdot m_2}}{{(\frac{r}{2})^2}} = G \frac{{m_1 \cdot m_2}}{{\frac{r^2}{4}}} = 4G \frac{{m_1 \cdot m_2}}{{r^2}} = 4F \)
Final Calculation of Gravitational Force
When both changes occur simultaneously:
- The new gravitational force \( F_{new} \) becomes:
\[ F_{new} = 2F \times 4 = 8F \]
Thus, the gravitational force will increase by a factor of **8** if the mass of one object is doubled and the separation between the two objects is halved.
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What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved?
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What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved?.
What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the gravitational force if the mass of one of the object is doubled and the separation between the two object is halved?.
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