Question

The value of acceleration due to gravity at a
depth of 1600 km is equal to
[Radius of earth = 6400 km]

(A) 9.8 ms -2

(B) 4.9 ms-2

(C) 19.6 ms-2

(D) 7.35 ms-2



( with method )​

Answer 1

Hi,

Here is your answer

Given:

Depth(d)=1600km=1600000m

Acceleration due to gravity on surface of earth(g)=9.8m/s²

Radius of earth(R)=6400km=6400000m

To Find:

Acceleration due to gravity at depth(g₁)

Solution:

Variation in acceleration due to gravity at depth d is given by

g₁=g(1-d/R)

Substituting the given dats, we get

g₁=9.8(1-1600000/6400000)

g₁=7.35m/s²

Hence the value of acceleration due to gravity at a depth of 1600 km is equal to 7.35m/s²

The correct option is D

Notes:

1.Acceleration due to gravity decreases with increase in depth and vice versa

2.Acceleration due to gravity decreases as we move away from,the earth's surface, that is when altitude increases.

Hope this helps you.