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A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.
The subsequent motion of the combined body will be :
The subsequent motion of the combined body will be :
- a)in a circular orbit of a different radius
- b)in the same circular orbit of radius R
- c)in an elliptical orbit
- d)such that it escapes to infinity
Correct answer is option 'C'. Can you explain this answer?
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A satellite of mass M is in a circular orbit of radius R about the cen...
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A satellite of mass M is in a circular orbit of radius R about the cen...
Explanation:
Before the collision, both the satellite and the meteorite are in a circular orbit of radius R around the center of the Earth. The speeds of the satellite and the meteorite are the same, which means they have the same kinetic energy.
Conservation of Momentum:
When the meteorite collides with the satellite, they stick together and form a combined body. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Since the satellite and the meteorite have the same mass and the same velocity before the collision, their momenta are equal and opposite. Therefore, the total momentum before the collision is zero.
After the collision, the satellite and the meteorite stick together and move as one body. Since the total momentum after the collision must also be zero, this means the combined body must have zero velocity.
Conservation of Energy:
The total energy of the system is conserved, which means the kinetic energy before the collision is equal to the kinetic energy after the collision. Since the speeds of the satellite and the meteorite are the same before the collision, their kinetic energies are also equal.
After the collision, the combined body has zero velocity, which means its kinetic energy is zero. Therefore, all the initial kinetic energy has been converted into another form of energy, such as potential energy or heat.
Subsequent Motion:
Since the combined body has zero velocity after the collision, it cannot remain in a circular orbit. Instead, it will move in an elliptical orbit around the center of the Earth.
The shape of the elliptical orbit will depend on the initial kinetic energy of the system. If the initial kinetic energy is greater than zero, the elliptical orbit will be elongated and the combined body will eventually return to the point of closest approach to the Earth (perigee) and continue in a periodic motion.
If the initial kinetic energy is exactly zero, the elliptical orbit will be a perfect circle with a radius equal to the original radius of the satellite's circular orbit.
Conclusion:
In conclusion, the subsequent motion of the combined body after the collision will be in an elliptical orbit around the center of the Earth. The shape of the elliptical orbit will depend on the initial kinetic energy of the system.
Before the collision, both the satellite and the meteorite are in a circular orbit of radius R around the center of the Earth. The speeds of the satellite and the meteorite are the same, which means they have the same kinetic energy.
Conservation of Momentum:
When the meteorite collides with the satellite, they stick together and form a combined body. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Since the satellite and the meteorite have the same mass and the same velocity before the collision, their momenta are equal and opposite. Therefore, the total momentum before the collision is zero.
After the collision, the satellite and the meteorite stick together and move as one body. Since the total momentum after the collision must also be zero, this means the combined body must have zero velocity.
Conservation of Energy:
The total energy of the system is conserved, which means the kinetic energy before the collision is equal to the kinetic energy after the collision. Since the speeds of the satellite and the meteorite are the same before the collision, their kinetic energies are also equal.
After the collision, the combined body has zero velocity, which means its kinetic energy is zero. Therefore, all the initial kinetic energy has been converted into another form of energy, such as potential energy or heat.
Subsequent Motion:
Since the combined body has zero velocity after the collision, it cannot remain in a circular orbit. Instead, it will move in an elliptical orbit around the center of the Earth.
The shape of the elliptical orbit will depend on the initial kinetic energy of the system. If the initial kinetic energy is greater than zero, the elliptical orbit will be elongated and the combined body will eventually return to the point of closest approach to the Earth (perigee) and continue in a periodic motion.
If the initial kinetic energy is exactly zero, the elliptical orbit will be a perfect circle with a radius equal to the original radius of the satellite's circular orbit.
Conclusion:
In conclusion, the subsequent motion of the combined body after the collision will be in an elliptical orbit around the center of the Earth. The shape of the elliptical orbit will depend on the initial kinetic energy of the system.
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A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.The subsequent motion of the combined body will be :a)in a circular orbit of a different radiusb)in the same circular orbit of radius Rc)in an elliptical orbitd)such that it escapes to infinityCorrect answer is option 'C'. Can you explain this answer?
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A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.The subsequent motion of the combined body will be :a)in a circular orbit of a different radiusb)in the same circular orbit of radius Rc)in an elliptical orbitd)such that it escapes to infinityCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.The subsequent motion of the combined body will be :a)in a circular orbit of a different radiusb)in the same circular orbit of radius Rc)in an elliptical orbitd)such that it escapes to infinityCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.The subsequent motion of the combined body will be :a)in a circular orbit of a different radiusb)in the same circular orbit of radius Rc)in an elliptical orbitd)such that it escapes to infinityCorrect answer is option 'C'. Can you explain this answer?.
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