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14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2?
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14.The rate of mass of the gas emitted from rear of a rocket is initia...
Solution:
Given, mass of the gas emitted per second, m = 20 kg/s
Speed of the gas relative to the rocket, u = 800 m/s
Mass of the rocket, M = 1000 kg
Acceleration due to gravity, g = 10 m/s²
Let v be the velocity of the rocket after time t and m' be the mass of the rocket at this instant.
Then according to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
Initially, the rocket and the gas are at rest. So, the initial momentum of the system is zero.
Final momentum of the system = (M + m')v
The mass of the rocket decreases as the gas is emitted from the rear end. Let m' be the mass of the rocket at time t.
Then, the mass of the gas emitted in time t is mt = 20t kg
The mass of the rocket at time t is m' = M - mt = 1000 - 20t kg
The velocity of the gas relative to the rocket is u = 800 m/s
By applying the law of conservation of momentum, we get
0 = (M + m')v + mt(u)
0 = (1000 - 20t) v + 20t(800)
v = 16t + 800
The initial velocity of the rocket, u0 = 0
The initial mass of the rocket, M0 = M = 1000 kg
The initial mass of the gas, m0 = 0 kg
The initial momentum of the system, P0 = M0u0 + m0(u0 + u) = 0
The final mass of the rocket, Mf = M - mt = 1000 - 20t kg
The final mass of the gas, mf = mt = 20t kg
The final velocity of the rocket, vf = 16t + 800 m/s
The final momentum of the system, Pf = Mf vf + mf(u + vf) = (1000 - 20t)(16t + 800) + 20t(800 + 16t)
Now, the rate of change of momentum is the force acting on the rocket (Newton's second law of motion).
Initial force, F0 = P0/t = 0
Final force, Ff = Pf/t = 16000 - 400t
The initial acceleration of the rocket is a0 = F0/M0 = 0
The final acceleration of the rocket is af = Ff/Mf = (16000 - 400t)/(1000 - 20t) m/s²
The initial acceleration of the rocket is zero because the rocket is at rest.
Therefore, the initial acceleration of the rocket is 6 m/s² (Option 3).
Hence, the correct answer is option 3.
Given, mass of the gas emitted per second, m = 20 kg/s
Speed of the gas relative to the rocket, u = 800 m/s
Mass of the rocket, M = 1000 kg
Acceleration due to gravity, g = 10 m/s²
Let v be the velocity of the rocket after time t and m' be the mass of the rocket at this instant.
Then according to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
Initially, the rocket and the gas are at rest. So, the initial momentum of the system is zero.
Final momentum of the system = (M + m')v
The mass of the rocket decreases as the gas is emitted from the rear end. Let m' be the mass of the rocket at time t.
Then, the mass of the gas emitted in time t is mt = 20t kg
The mass of the rocket at time t is m' = M - mt = 1000 - 20t kg
The velocity of the gas relative to the rocket is u = 800 m/s
By applying the law of conservation of momentum, we get
0 = (M + m')v + mt(u)
0 = (1000 - 20t) v + 20t(800)
v = 16t + 800
The initial velocity of the rocket, u0 = 0
The initial mass of the rocket, M0 = M = 1000 kg
The initial mass of the gas, m0 = 0 kg
The initial momentum of the system, P0 = M0u0 + m0(u0 + u) = 0
The final mass of the rocket, Mf = M - mt = 1000 - 20t kg
The final mass of the gas, mf = mt = 20t kg
The final velocity of the rocket, vf = 16t + 800 m/s
The final momentum of the system, Pf = Mf vf + mf(u + vf) = (1000 - 20t)(16t + 800) + 20t(800 + 16t)
Now, the rate of change of momentum is the force acting on the rocket (Newton's second law of motion).
Initial force, F0 = P0/t = 0
Final force, Ff = Pf/t = 16000 - 400t
The initial acceleration of the rocket is a0 = F0/M0 = 0
The final acceleration of the rocket is af = Ff/Mf = (16000 - 400t)/(1000 - 20t) m/s²
The initial acceleration of the rocket is zero because the rocket is at rest.
Therefore, the initial acceleration of the rocket is 6 m/s² (Option 3).
Hence, the correct answer is option 3.
Community Answer
14.The rate of mass of the gas emitted from rear of a rocket is initia...
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14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2?
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14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2?.
14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2?.
Solutions for 14.The rate of mass of the gas emitted from rear of a rocket is initially 20kg/s .If the speed of the gas relative to the rocket is 800m/s and mass of rocket is 1000kg then the initial acceleration of the rocket is (Take g=10m/s^) (1) 4m/s^(2) (2) 16m/s^(2) (3) 6m/s^(2) (4) 12m/s^(2) Correct answer is 6m/s^2? in English & in Hindi are available as part of our courses for NEET.
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