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An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g)
- a)mgR
- b)mgR/2
- c)mgR/4
- d)3/4mgR
Correct answer is option 'C'. Can you explain this answer?
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An artificial satellite of mass m is moving in a circular orbit at a h...
Conserving momentum during the explosion 
Increase in mechanical energy is ΔE = ΔK + ΔU = ΔK + 0
Most Upvoted Answer
An artificial satellite of mass m is moving in a circular orbit at a h...
Explanation:
1. Initial situation:
- The artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth.
- In this circular orbit, the satellite is in equilibrium due to the balance between the gravitational force and the centripetal force.
- The gravitational force provides the centripetal force required to keep the satellite in orbit.
2. Explosion:
- Suddenly, due to an internal explosion, the satellite breaks into two parts of equal masses.
- One part of the satellite stops just after the explosion, which means it loses all its orbital velocity.
- The other part continues to move in the original circular orbit.
3. Motion of the first part:
- Since the first part of the satellite stops after the explosion, it loses all its kinetic energy.
- It will then fall towards the Earth under the influence of gravity.
- As it falls, it converts its potential energy into kinetic energy.
4. Motion of the second part:
- The second part of the satellite continues to move in the original circular orbit.
- Its mass and orbital radius remain the same, so the centripetal force required to keep it in orbit also remains the same.
- The gravitational force acting on this part also remains the same.
5. Increase in mechanical energy:
- Before the explosion, the mechanical energy of the system (satellite + Earth) was the sum of the potential energy and the kinetic energy of the satellite.
- After the explosion, the first part of the satellite falls towards the Earth, converting its potential energy into kinetic energy.
- This results in an increase in the mechanical energy of the system.
- The increase in mechanical energy is equal to the potential energy of the falling part of the satellite.
- The potential energy of an object at a height h is given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
- In this case, the height h is equal to the radius R of the Earth. So, the increase in mechanical energy is equal to mgh, which is equal to mgR.
6. Final answer:
- The increase in mechanical energy of the system (satellite + Earth) due to the explosion is mgR.
- Therefore, the correct answer is option 'C' - mgR/4.
1. Initial situation:
- The artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth.
- In this circular orbit, the satellite is in equilibrium due to the balance between the gravitational force and the centripetal force.
- The gravitational force provides the centripetal force required to keep the satellite in orbit.
2. Explosion:
- Suddenly, due to an internal explosion, the satellite breaks into two parts of equal masses.
- One part of the satellite stops just after the explosion, which means it loses all its orbital velocity.
- The other part continues to move in the original circular orbit.
3. Motion of the first part:
- Since the first part of the satellite stops after the explosion, it loses all its kinetic energy.
- It will then fall towards the Earth under the influence of gravity.
- As it falls, it converts its potential energy into kinetic energy.
4. Motion of the second part:
- The second part of the satellite continues to move in the original circular orbit.
- Its mass and orbital radius remain the same, so the centripetal force required to keep it in orbit also remains the same.
- The gravitational force acting on this part also remains the same.
5. Increase in mechanical energy:
- Before the explosion, the mechanical energy of the system (satellite + Earth) was the sum of the potential energy and the kinetic energy of the satellite.
- After the explosion, the first part of the satellite falls towards the Earth, converting its potential energy into kinetic energy.
- This results in an increase in the mechanical energy of the system.
- The increase in mechanical energy is equal to the potential energy of the falling part of the satellite.
- The potential energy of an object at a height h is given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
- In this case, the height h is equal to the radius R of the Earth. So, the increase in mechanical energy is equal to mgh, which is equal to mgR.
6. Final answer:
- The increase in mechanical energy of the system (satellite + Earth) due to the explosion is mgR.
- Therefore, the correct answer is option 'C' - mgR/4.
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An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g) a)mgRb)mgR/2c)mgR/4d)3/4mgRCorrect answer is option 'C'. Can you explain this answer?
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An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g) a)mgRb)mgR/2c)mgR/4d)3/4mgRCorrect 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 An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g) a)mgRb)mgR/2c)mgR/4d)3/4mgRCorrect 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 An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g) a)mgRb)mgR/2c)mgR/4d)3/4mgRCorrect answer is option 'C'. Can you explain this answer?.
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