
Discuss the variation of acceleration due to gravity with depth. What happens to g at the center of the Earth.
Answer
523.2k+ views
7 likes
Hint: Acceleration due to gravity depends on distance from the center of the Earth. Replace R by (R-d) as distance from center decreases as we move towards center.
Complete step by step answer:
Acceleration due to gravity is acceleration gained by an object while moving under the influence of gravitational force.
On the Earth’s surface it is given as
Where, G is universal constant of gravitation
M is Mass of earth
R is radius of earth
If is the density of earth then
Therefore,
…...….……………………………….(1)
Now if a body is taken to depth d then
……………………………….(2)
Dividing equation (2) by equation (1)
This an expression for acceleration due to gravity at depth d.
From equation (2) we can say that as depth increases acceleration due to gravity decreases and at the center as d=R, acceleration due gravity becomes zero.
Therefore, at center of Earth as d=R
Acceleration due to gravity decreases linearly with increase in depth.
Additional Information:
Acceleration due to gravity also decreases as we move above Earth’s surface. Thus, acceleration due to gravity is maximum at the Earth’s surface and is zero at the center of the Earth and at infinite distance above the Earth’s surface.
Note: No need to remember the whole derivation, just remember to replace R by (R-d) where d is depth. Further calculation is just a simple mathematical manipulation. Once you have obtained expression for acceleration due to gravity at depth d then compare it with acceleration due to gravity at earth’s surface.
Complete step by step answer:
Acceleration due to gravity is acceleration gained by an object while moving under the influence of gravitational force.
On the Earth’s surface it is given as
Where, G is universal constant of gravitation
M is Mass of earth
R is radius of earth
If
Therefore,
Now if a body is taken to depth d then
Dividing equation (2) by equation (1)
This an expression for acceleration due to gravity at depth d.
From equation (2) we can say that as depth increases acceleration due to gravity decreases and at the center as d=R, acceleration due gravity becomes zero.
Therefore, at center of Earth as d=R
Acceleration due to gravity decreases linearly with increase in depth.
Additional Information:
Acceleration due to gravity also decreases as we move above Earth’s surface. Thus, acceleration due to gravity is maximum at the Earth’s surface and is zero at the center of the Earth and at infinite distance above the Earth’s surface.
Note: No need to remember the whole derivation, just remember to replace R by (R-d) where d is depth. Further calculation is just a simple mathematical manipulation. Once you have obtained expression for acceleration due to gravity at depth d then compare it with acceleration due to gravity at earth’s surface.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
How many moles and how many grams of NaCl are present class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Plants which grow in shade are called A Sciophytes class 11 biology CBSE

A renewable exhaustible natural resource is A Petroleum class 11 biology CBSE

In which of the following gametophytes is not independent class 11 biology CBSE

Find the molecular mass of Sulphuric Acid class 11 chemistry CBSE
