Question

At what depth below the surface of earth, value of accelaration due to gravity is same as the value at height h =R1, where R is the radius of earth.

Answer 1

Explanation:

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At what height above the surface will the acceleration due to gravity be one fourth of its value on the surface of the earth?

12 Answers

Rashmita Pradhan

Rashmita Pradhan, As a student of physics

Answered Nov 17, 2016 · Author has 145 answers and 271.6k answer views

For this question,

We have the formula, g' = g/(1+h/R)^2

Here g' = acceleration due to gravity at the height

g = 9.8m/s^2

R = radius of earth

h = height

g/g' = (1+h/R)^2

4 = (1+h/R )^2

1+h/R = 2

h/R = 1

h = R

So at the height of 6371 km the value of g is 1/4 th of its original value .

Answer 2

Given :

Acceleration due to gravity = g

height = h

Radius of earth = R

To find :

The depth below the surface of the earth where acceleration due to gravity is same at height h=R1

Solution :

• Acceleration due to gravity at height h = g/(1+h/R)²………(1)

• Acceleration due to gravity at depth d = g(1-d/R)…………(2)

• By equating both the equations

       g/(1+h/r)² = g(1-d/r)

• By substituing h= R, we get

                       d=3/4R

• At a depth of d=3/4R the acceleration due to gravity is same as that of height h=R