Question

Assuming the radius of earth to be 6400 km. calculate the
depth from the earth surface at which the value of acceleration
due to gravity will reduce to half.
please give the answer fast .​

Answer 1

Answer:-

At a depth of 3200km from the surface of earth, the value of acceleration due to gravity will reduce to half.

Explaination:-

We know that, variation in acceleration due to gravity with depth below the earth's surface is given by :-

g' = g(1 - d/Rₑ)

Where :-

• g' is the acceleration due to gravity at

given depth from the surface of earth.

• g is acceleration due to gravity at the

surface of earth.

• d is the depth from the earth's surface.

• Rₑ is the radius of the eath.

Here, in this case :-

• g' = g/2

• Rₑ = 6400km

And, we require to calculate 'd'.

So, by substituting values,we get :-

=> g/2 = g(1 - d/6400)

=> g/2 = g(6400 - d/6400)

=> 1/2 = 6400 - d/6400

=> 6400 = 2(6400 - d)

=> 6400 = 12800 - 2d

=> 6400 - 12800 = -2d

=> -6400 = -2d

=> d = -6400/-2

=> d = 3200 km