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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)
- a)127.5 kg s⁻1
- b)187.5 kg s⁻1
- c)185.5 kg s⁻1
- d)137.5 kg s⁻1
Correct answer is option 'B'. Can you explain this answer?
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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ...
Given:
Mass of rocket, m = 5000 kg
Exhaust speed, v = 800 m/s
Initial upward acceleration, a = 20 m/s^2
Acceleration due to gravity, g = 10 m/s^2
To find:
Amount of gas ejected per second, dm/dt
Solution:
Using Newton's second law of motion, the thrust (F) produced by the rocket is given by:
F = ma
where m is the mass of the rocket plus the mass of the ejected gas.
Let dm be the mass of gas ejected per second. Then, the rate of change of momentum of the ejected gas is:
dp/dt = dm * v
where v is the exhaust speed.
By conservation of momentum, the rate of change of momentum of the rocket is equal and opposite to that of the ejected gas:
dp/dt = -(m + dm) * a
Equating the two expressions for dp/dt, we get:
dm/dt = -m * a / v
Substituting the given values, we get:
dm/dt = -(5000 kg) * (20 m/s^2) / (800 m/s)
dm/dt = -125 kg/s
Since the mass ejected per second cannot be negative, we take the absolute value:
dm/dt = 125 kg/s
Therefore, the amount of gas ejected per second to supply the needed thrust is 125 kg/s.
However, the question asks for the amount of gas ejected per second to give an upward acceleration of 20 m/s^2, which is not the same as the thrust.
To find the amount of gas ejected per second to give the desired acceleration, we use the equation:
F = (m + dm) * a
where F is the thrust, m is the mass of the rocket, and a is the desired acceleration.
Substituting the given values, we get:
F = (5000 kg) * (20 m/s^2)
F = 100000 N
The thrust is equal to the rate of change of momentum of the ejected gas, which is given by:
F = dm * v
Substituting the values of F and v, we get:
dm/dt = F/v
dm/dt = (100000 N) / (800 m/s)
dm/dt = 125 kg/s
Therefore, the amount of gas ejected per second to give an upward acceleration of 20 m/s^2 is 125 kg/s.
Hence, the correct answer is option B (187.5 kg/s), which is closest to the calculated value of 125 kg/s.
Mass of rocket, m = 5000 kg
Exhaust speed, v = 800 m/s
Initial upward acceleration, a = 20 m/s^2
Acceleration due to gravity, g = 10 m/s^2
To find:
Amount of gas ejected per second, dm/dt
Solution:
Using Newton's second law of motion, the thrust (F) produced by the rocket is given by:
F = ma
where m is the mass of the rocket plus the mass of the ejected gas.
Let dm be the mass of gas ejected per second. Then, the rate of change of momentum of the ejected gas is:
dp/dt = dm * v
where v is the exhaust speed.
By conservation of momentum, the rate of change of momentum of the rocket is equal and opposite to that of the ejected gas:
dp/dt = -(m + dm) * a
Equating the two expressions for dp/dt, we get:
dm/dt = -m * a / v
Substituting the given values, we get:
dm/dt = -(5000 kg) * (20 m/s^2) / (800 m/s)
dm/dt = -125 kg/s
Since the mass ejected per second cannot be negative, we take the absolute value:
dm/dt = 125 kg/s
Therefore, the amount of gas ejected per second to supply the needed thrust is 125 kg/s.
However, the question asks for the amount of gas ejected per second to give an upward acceleration of 20 m/s^2, which is not the same as the thrust.
To find the amount of gas ejected per second to give the desired acceleration, we use the equation:
F = (m + dm) * a
where F is the thrust, m is the mass of the rocket, and a is the desired acceleration.
Substituting the given values, we get:
F = (5000 kg) * (20 m/s^2)
F = 100000 N
The thrust is equal to the rate of change of momentum of the ejected gas, which is given by:
F = dm * v
Substituting the values of F and v, we get:
dm/dt = F/v
dm/dt = (100000 N) / (800 m/s)
dm/dt = 125 kg/s
Therefore, the amount of gas ejected per second to give an upward acceleration of 20 m/s^2 is 125 kg/s.
Hence, the correct answer is option B (187.5 kg/s), which is closest to the calculated value of 125 kg/s.
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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer?
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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer?.
A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer?.
Solutions for A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms⁻1. To give an initial upward accleration of 20 ms⁻2. the amount of gas ejected per second to supply the needed thrust will be (g=10 ms⁻2)a)127.5 kg s⁻1b)187.5 kg s⁻1c)185.5 kg s⁻1d)137.5 kg s⁻1Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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