The value of acceleration due to gravity at a depth of 1600km is equal to Radius of the Earth=6400km

We may apply the formula for acceleration due to gravity at any location inside the earth to get the value of acceleration due to gravity at a depth of 1600 km. We are aware that the acceleration caused by gravity is 9.8ms^-2 at the earth's surface.

The planet Earth can be seen as a solid sphere with a homogeneous distribution of mass. The formula provides the gravitational field or gravitational acceleration at every location on the earth.

$g_r=\frac{GMr}{R^3}$

Where M is the mass of the earth, R is its radius, and r is the distance from the planet's centre. G is the universal gravitational constant.
Let's define g as the acceleration caused by gravity at the surface of the earth. The value of g is given by the formula for the acceleration caused by gravity at every location on Earth:

$g=\frac{GMR}{R^3}=\frac{GM}{R^2}$

Also, we know that

A point's distance from the centre is Rd if it is at depth d. Therefore, the current rate of gravity's acceleration is (using formula of acceleration due to gravity at any point inside the earth)

$g_d=\frac{GMr}{R^3}=\frac{GM(R-d)}{R^3}=\frac{GM}{R^2}\left(1-\frac{d}{R}\right)$

$g_d=g\left(1-\frac{d}{R}\right)$

The radius of the earth is provided to us as 6400 km, and we must locate a gravitational field at a distance from the surface of the earth of 1600 km. Thus, by using these values in the equation above, we obtain

$g_d=9.8\left(1-\frac{1600}{6400}\right)=7.35{\mathrm{ss}}^{-2}$

The correct answer is option C) g_d=7.35ms⁻²