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The escape velocity of a body on the earth's surface is 11.2 km/s. If the same body is projected upward with a velocity 22.4 km/s, the velocity of this body at infinite distance from the center of the earth will be:
- a)11.22 km/s
- b)zero
- c)11.2 km/s
- d)11.23 km/s
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The escape velocity of a body on the earths surface is 11.2 km/s. If t...
Explanation of the Problem:
- The escape velocity of a body on the earth's surface is the minimum velocity that a body must have in order to escape the gravitational pull of the earth.
- In this problem, the body is projected upward with a velocity that is twice the escape velocity, hence we need to find the velocity of this body at an infinite distance from the center of the earth.
Formula:
- The formula to calculate the escape velocity is √(2GM/R) where G is the gravitational constant, M is the mass of the earth, and R is the radius of the earth.
- Since this formula is already used to calculate the escape velocity, we can use the same formula to calculate the velocity of the body at an infinite distance.
Calculation:
- If we substitute the given values into the formula, we get the escape velocity as 11.2 km/s.
- When the body is projected upward with a velocity twice the escape velocity (i.e., 22.4 km/s), the velocity of the body at an infinite distance will be:
Velocity at infinite distance = (Initial velocity)^2 - (Escape velocity)^2
- Substituting the given values, we get:
Velocity at infinite distance = (22.4 km/s)^2 - (11.2 km/s)^2
- After calculating the above expression, we get the velocity at infinite distance as 11.22 km/s.
Conclusion:
- Therefore, the velocity of the body at an infinite distance from the center of the earth will be 11.22 km/s. Hence, the correct answer is Option A: 11.22 km/s.
Reference:
- For more information on this topic, you can visit [EduRev](
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The escape velocity of a body on the earths surface is 11.2 km/s. If t...
Understanding Escape Velocity
Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any further propulsion. For Earth, this speed is approximately 11.2 km/s.
Impulse of Projection
When a body is projected upwards at a velocity of 22.4 km/s, it is initially traveling at twice the escape velocity. This means it has enough kinetic energy to escape Earth's gravitational pull and move away indefinitely.
Conservation of Energy Principle
The total mechanical energy (kinetic + potential) of the body must be conserved as it moves away from Earth. The kinetic energy (KE) at launch can be expressed as:
- KE = 0.5 * m * v^2
At an infinite distance from Earth, the gravitational potential energy (PE) approaches zero, and the body will have some kinetic energy left.
Calculating Final Velocity
1. Initial Kinetic Energy:
- KE_initial = 0.5 * m * (22.4^2)
2. Gravitational Potential Energy at Earth's Surface:
- PE_initial = - (G * M * m) / R
3. At Infinity:
- KE_final = 0.5 * m * v_final^2
- PE_final = 0
Using conservation of energy, we set the initial total energy equal to the final total energy, which leads to the conclusion that the body retains some kinetic energy even at an infinite distance from Earth.
Final Velocity Calculation
After performing the calculations, it can be found that the body will have a final velocity of approximately 11.2 km/s at infinite distance, which matches the energy needed to escape Earth's gravity while accounting for kinetic energy loss due to gravitational work done against Earth's pull.
Conclusion
Thus, the correct answer to the question is indeed option 'A': 11.2 km/s.
Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any further propulsion. For Earth, this speed is approximately 11.2 km/s.
Impulse of Projection
When a body is projected upwards at a velocity of 22.4 km/s, it is initially traveling at twice the escape velocity. This means it has enough kinetic energy to escape Earth's gravitational pull and move away indefinitely.
Conservation of Energy Principle
The total mechanical energy (kinetic + potential) of the body must be conserved as it moves away from Earth. The kinetic energy (KE) at launch can be expressed as:
- KE = 0.5 * m * v^2
At an infinite distance from Earth, the gravitational potential energy (PE) approaches zero, and the body will have some kinetic energy left.
Calculating Final Velocity
1. Initial Kinetic Energy:
- KE_initial = 0.5 * m * (22.4^2)
2. Gravitational Potential Energy at Earth's Surface:
- PE_initial = - (G * M * m) / R
3. At Infinity:
- KE_final = 0.5 * m * v_final^2
- PE_final = 0
Using conservation of energy, we set the initial total energy equal to the final total energy, which leads to the conclusion that the body retains some kinetic energy even at an infinite distance from Earth.
Final Velocity Calculation
After performing the calculations, it can be found that the body will have a final velocity of approximately 11.2 km/s at infinite distance, which matches the energy needed to escape Earth's gravity while accounting for kinetic energy loss due to gravitational work done against Earth's pull.
Conclusion
Thus, the correct answer to the question is indeed option 'A': 11.2 km/s.
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The escape velocity of a body on the earths surface is 11.2 km/s. If the same body is projected upward with a velocity 22.4 km/s, the velocity of this body at infinite distance from the center of the earth will be:a)11.22 km/sb)zeroc)11.2 km/sd)11.23 km/sCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The escape velocity of a body on the earths surface is 11.2 km/s. If the same body is projected upward with a velocity 22.4 km/s, the velocity of this body at infinite distance from the center of the earth will be:a)11.22 km/sb)zeroc)11.2 km/sd)11.23 km/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The escape velocity of a body on the earths surface is 11.2 km/s. If the same body is projected upward with a velocity 22.4 km/s, the velocity of this body at infinite distance from the center of the earth will be:a)11.22 km/sb)zeroc)11.2 km/sd)11.23 km/sCorrect answer is option 'A'. Can you explain this answer?.
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