NEET Exam > NEET Questions > The height at which the acceleration due togr...
Start Learning for Free
The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is
- a)R/√2
- b)R/2
- c)√2 R
- d)2 R
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The height at which the acceleration due togravity becomes g/9(where g...
To find the height at which the acceleration due to gravity becomes g/9, we need to equate the gravitational force at that height to the centripetal force required for circular motion at that height.
At a height h above the surface of the Earth, the gravitational force can be calculated using the formula:
F = (GMm) / (R+h)^2
Where:
G is the gravitational constant
M is the mass of the Earth
m is the mass of the object experiencing gravity
R is the radius of the Earth
h is the height above the surface of the Earth
The centripetal force required for circular motion at that height is given by:
F = (mv^2) / (R+h)
Where:
m is the mass of the object experiencing circular motion
v is the velocity of the object experiencing circular motion
Since we are looking for the height at which the acceleration due to gravity becomes g/9, we can set these two forces equal to each other:
(GMm) / (R+h)^2 = (mv^2) / (R+h)
Canceling out the mass (m) and velocity (v) terms, we get:
GM / (R+h)^2 = v^2 / (R+h)
Since the acceleration due to gravity at that height is g/9, we can substitute g/9 for v^2:
GM / (R+h)^2 = (g/9) / (R+h)
Cross multiplying and simplifying, we get:
9GM = g(R+h)
Dividing both sides by g, we get:
9M = R+h
Rearranging the equation, we get:
h = 9M - R
Therefore, the height at which the acceleration due to gravity becomes g/9 is 9M - R.
At a height h above the surface of the Earth, the gravitational force can be calculated using the formula:
F = (GMm) / (R+h)^2
Where:
G is the gravitational constant
M is the mass of the Earth
m is the mass of the object experiencing gravity
R is the radius of the Earth
h is the height above the surface of the Earth
The centripetal force required for circular motion at that height is given by:
F = (mv^2) / (R+h)
Where:
m is the mass of the object experiencing circular motion
v is the velocity of the object experiencing circular motion
Since we are looking for the height at which the acceleration due to gravity becomes g/9, we can set these two forces equal to each other:
(GMm) / (R+h)^2 = (mv^2) / (R+h)
Canceling out the mass (m) and velocity (v) terms, we get:
GM / (R+h)^2 = v^2 / (R+h)
Since the acceleration due to gravity at that height is g/9, we can substitute g/9 for v^2:
GM / (R+h)^2 = (g/9) / (R+h)
Cross multiplying and simplifying, we get:
9GM = g(R+h)
Dividing both sides by g, we get:
9M = R+h
Rearranging the equation, we get:
h = 9M - R
Therefore, the height at which the acceleration due to gravity becomes g/9 is 9M - R.
Free Test
FREE
| Start Free Test |
Community Answer
The height at which the acceleration due togravity becomes g/9(where g...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer?
Question Description
The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect 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 The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect 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 The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer?.
The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect 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 The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect 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 The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The height at which the acceleration due togravity becomes g/9(where g = the accelerationdue to gravity on the surface of the earth) in terms of R, the radius of the earth, isa)R/√2b)R/2c)√2 Rd)2 RCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup