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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of
- a)1 : √2
- b)√2 : 1
- c)1 : 4
- d)1 : 2
Correct answer is option 'D'. Can you explain this answer?
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A ball of mass 2 kg and another of mass 4 kg are dropped together fro...
Given:
Mass of first ball, m1 = 2 kg
Mass of second ball, m2 = 4 kg
Height of building, h = 60 feet
Height of fall, h1 = h2 = 30 feet
To find:
Ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth.
Solution:
1. Potential energy at the top of the building = mgh
Potential energy at the top of the building = (2+4) x 9.8 x 60 = 3528 J
2. Potential energy after falling through 30 feet = mgh
Potential energy after falling through 30 feet = (2+4) x 9.8 x 30 = 1764 J
3. Kinetic energy after falling through 30 feet = Potential energy at the top - Potential energy after falling through 30 feet
Kinetic energy of first ball after falling through 30 feet = 3528 - 1764 = 1764 J
Kinetic energy of second ball after falling through 30 feet = 3528 - 1764 = 1764 J
4. Ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth
Ratio of kinetic energies = KE1/KE2
KE1/KE2 = (1/2) m1v1^2 / (1/2) m2v2^2
KE1/KE2 = m1v1^2 / m2v2^2
Velocity v of a ball after falling through a height h can be calculated using the formula v = sqrt(2gh)
v1 = sqrt(2gh1) and v2 = sqrt(2gh2)
KE1/KE2 = m1(2gh1) / m2(2gh2)
KE1/KE2 = m1/m2 x h1/h2
KE1/KE2 = 2/4 x 30/30
KE1/KE2 = 1/2
Therefore, the ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth is 1:2. Hence, option D is the correct answer.
Mass of first ball, m1 = 2 kg
Mass of second ball, m2 = 4 kg
Height of building, h = 60 feet
Height of fall, h1 = h2 = 30 feet
To find:
Ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth.
Solution:
1. Potential energy at the top of the building = mgh
Potential energy at the top of the building = (2+4) x 9.8 x 60 = 3528 J
2. Potential energy after falling through 30 feet = mgh
Potential energy after falling through 30 feet = (2+4) x 9.8 x 30 = 1764 J
3. Kinetic energy after falling through 30 feet = Potential energy at the top - Potential energy after falling through 30 feet
Kinetic energy of first ball after falling through 30 feet = 3528 - 1764 = 1764 J
Kinetic energy of second ball after falling through 30 feet = 3528 - 1764 = 1764 J
4. Ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth
Ratio of kinetic energies = KE1/KE2
KE1/KE2 = (1/2) m1v1^2 / (1/2) m2v2^2
KE1/KE2 = m1v1^2 / m2v2^2
Velocity v of a ball after falling through a height h can be calculated using the formula v = sqrt(2gh)
v1 = sqrt(2gh1) and v2 = sqrt(2gh2)
KE1/KE2 = m1(2gh1) / m2(2gh2)
KE1/KE2 = m1/m2 x h1/h2
KE1/KE2 = 2/4 x 30/30
KE1/KE2 = 1/2
Therefore, the ratio of kinetic energies of the two balls after falling through 30 feet each towards the earth is 1:2. Hence, option D is the correct answer.
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Community Answer
A ball of mass 2 kg and another of mass 4 kg are dropped together fro...
Since height is same for both balls, their velocities on reaching the ground will be same
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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer?
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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. 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 ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. 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 ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer?.
A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. 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 ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. 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 ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer?.
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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio ofa)1 : √2b)√2 : 1c)1 : 4d)1 : 2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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