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Two bodies of masses m1 and m2 are sepa...

Two bodies of masses `m_1 and m_2` are separated by certain distance. If `vecF_(12)` is the force on `m_1` due to `m_2 and vecF_(21)` is the force on `m_2` due to `m_1` then

A

`F_(12) = F_(21)`

B

`vecF_(12) = F_(21)`

C

`vecF_(12) = -F_(21)`

D

both 1 & 3

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the forces acting between two masses \( m_1 \) and \( m_2 \) that are separated by a distance \( r \). The forces \( \vec{F}_{12} \) and \( \vec{F}_{21} \) represent the gravitational force exerted by mass \( m_2 \) on mass \( m_1 \) and the gravitational force exerted by mass \( m_1 \) on mass \( m_2 \), respectively. ### Step-by-Step Solution: 1. **Understanding Newton's Third Law**: According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that the force exerted by \( m_2 \) on \( m_1 \) is equal in magnitude and opposite in direction to the force exerted by \( m_1 \) on \( m_2 \). \[ \vec{F}_{12} = -\vec{F}_{21} \] 2. **Magnitude of Forces**: The magnitudes of the forces can be expressed as: \[ |\vec{F}_{12}| = |\vec{F}_{21}| \] This indicates that the forces are equal in magnitude. 3. **Vector Representation**: If we consider the direction of the forces, we can represent them as: - Let \( \vec{F}_{12} \) be directed towards \( m_2 \) (the force on \( m_1 \) due to \( m_2 \)). - Let \( \vec{F}_{21} \) be directed towards \( m_1 \) (the force on \( m_2 \) due to \( m_1 \)). Therefore, we can write: \[ \vec{F}_{12} = -\vec{F}_{21} \] 4. **Conclusion**: From the above analysis, we can conclude that: - The forces are equal in magnitude but opposite in direction. - This confirms that \( \vec{F}_{12} \) and \( \vec{F}_{21} \) are related by the equation \( \vec{F}_{12} = -\vec{F}_{21} \). ### Final Answer: Both statements \( |\vec{F}_{12}| = |\vec{F}_{21}| \) and \( \vec{F}_{12} = -\vec{F}_{21} \) are true.
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