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Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let w be the angular velocity of the earth's rotation about its ax...
Let, ge be the acceleration due to gravity on surface of earth, g′ be the acceleration due to gravity at depth d below the surface of earth and is given by
g′=ge(1−d/R) ............................(1)
The acceleration due to gravity of an object on latitude(below the surface of earth) is
g′=ge−ω2Rcosϕ
where, ϕ is the solid angle at the centre of earth sustained by the object.
At the equator, ϕ=0∘
∴cosϕ=1
Hence,
g′=ge−ω2R ...............(2)
From (1) and (2), we can write
ge(1−d/R)=ge−ω2R
⇒dge=ω2R
⇒d= ω2R2/ ge
g′=ge(1−d/R) ............................(1)
The acceleration due to gravity of an object on latitude(below the surface of earth) is
g′=ge−ω2Rcosϕ
where, ϕ is the solid angle at the centre of earth sustained by the object.
At the equator, ϕ=0∘
∴cosϕ=1
Hence,
g′=ge−ω2R ...............(2)
From (1) and (2), we can write
ge(1−d/R)=ge−ω2R
⇒dge=ω2R
⇒d= ω2R2/ ge
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Let w be the angular velocity of the earth's rotation about its ax...
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Let w be the angular velocity of the earth's rotation about its ax...
Let, ge be the acceleration due to gravity on surface of earth, g′ be the acceleration due to gravity at depth d below the surface of earth and is given by
g′=ge(1−d/R) ............................(1)
The acceleration due to gravity of an object on latitude(below the surface of earth) is
g′=ge−ω2Rcosϕ
where, ϕ is the solid angle at the centre of earth sustained by the object.
At the equator, ϕ=0∘
∴cosϕ=1
Hence,
g′=ge−ω2R ...............(2)
From (1) and (2), we can write
ge(1−d/R)=ge−ω2R
⇒dge=ω2R
⇒d= ω2R2/ ge
g′=ge(1−d/R) ............................(1)
The acceleration due to gravity of an object on latitude(below the surface of earth) is
g′=ge−ω2Rcosϕ
where, ϕ is the solid angle at the centre of earth sustained by the object.
At the equator, ϕ=0∘
∴cosϕ=1
Hence,
g′=ge−ω2R ...............(2)
From (1) and (2), we can write
ge(1−d/R)=ge−ω2R
⇒dge=ω2R
⇒d= ω2R2/ ge
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Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let w be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole (d << R). The value of d isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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