Question:
The orbital angular momentum of a satellite revolving at a distance \( r \) from the center is \( L \). If the distance is increased to \( 16r \), then the new angular momentum will be:
The orbital angular momentum of a satellite revolving at a distance \( r \) from the center is \( L \). If the distance is increased to \( 16r \), then the new angular momentum will be:
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The angular momentum of a satellite depends on both the distance from the center and the square root of the distance. If the distance is increased by a factor, the angular momentum changes by the square root of that factor.
Updated On: Apr 22, 2026
- 16 L
- 64 L
- \( \frac{L}{4} \)
- 4 L
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The Correct Option is D
Solution and Explanation
Step 1: Formula for Angular Momentum.
The orbital angular momentum \( L \) of a satellite moving in a circular orbit is given by: \[ L = m v r \] where \( m \) is the mass of the satellite, \( v \) is its velocity, and \( r \) is the distance from the center of the orbit.
Step 2: Relationship Between Angular Momentum and Distance.
The orbital velocity of the satellite is related to the gravitational force acting on it. The velocity of a satellite moving in a circular orbit is given by: \[ v = \sqrt{\frac{GM}{r}} \] where \( G \) is the gravitational constant and \( M \) is the mass of the central body (e.g., Earth). Substituting this into the expression for \( L \): \[ L = m \cdot \sqrt{\frac{GM}{r}} \cdot r \] Simplifying the expression: \[ L = m \cdot \sqrt{GM \cdot r} \]
Step 3: New Angular Momentum with Increased Distance.
Now, if the distance is increased to \( 16r \), the new angular momentum \( L' \) will be: \[ L' = m \cdot \sqrt{GM \cdot 16r} = m \cdot \sqrt{16 \cdot GM \cdot r} = 4 \cdot m \cdot \sqrt{GM \cdot r} \] Thus, the new angular momentum \( L' = 4L \).
Step 4: Conclusion.
Therefore, the new angular momentum is \( 4L \).
The orbital angular momentum \( L \) of a satellite moving in a circular orbit is given by: \[ L = m v r \] where \( m \) is the mass of the satellite, \( v \) is its velocity, and \( r \) is the distance from the center of the orbit.
Step 2: Relationship Between Angular Momentum and Distance.
The orbital velocity of the satellite is related to the gravitational force acting on it. The velocity of a satellite moving in a circular orbit is given by: \[ v = \sqrt{\frac{GM}{r}} \] where \( G \) is the gravitational constant and \( M \) is the mass of the central body (e.g., Earth). Substituting this into the expression for \( L \): \[ L = m \cdot \sqrt{\frac{GM}{r}} \cdot r \] Simplifying the expression: \[ L = m \cdot \sqrt{GM \cdot r} \]
Step 3: New Angular Momentum with Increased Distance.
Now, if the distance is increased to \( 16r \), the new angular momentum \( L' \) will be: \[ L' = m \cdot \sqrt{GM \cdot 16r} = m \cdot \sqrt{16 \cdot GM \cdot r} = 4 \cdot m \cdot \sqrt{GM \cdot r} \] Thus, the new angular momentum \( L' = 4L \).
Step 4: Conclusion.
Therefore, the new angular momentum is \( 4L \).
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