Question

show that the value of acceleration due to gravity with depth​

Answer 1

Factor affecting rate of reaction

Answer 2

Let’s say, a body of mass m is resting at point A , where A is at a depth of h from the earth’s surface.

Distance of point A from the centre of the earth = R – h,

where R is the radius of the earth.

acceleration due to gravity at a depth

Mass of inner sphere = (4/3). Pi. (R-h)^3. p

Here p is the density.

Now at point A, the gravitational force on the object of mass m is

F = G M m/ (R-h)^2 = G. [(4/3). Pi. (R-h)^3. p] m/(R-h)^2 = G. (4/3). Pi. (R-h). p. m

 

Again at point A, the acceleration due to gravity (say g2) = F/m = G. (4/3). Pi. (R-h). p  _________________ (7)

Now we know at earth’s surface, acceleration due to gravity = g = (4/3) Pi R p G

Taking the ratio, again,

g2/g = [G. (4/3). Pi. (R-h). p ] / [(4/3) Pi R p G] = (R-h) / R = 1 – h/R.

=> g2 = g (1 – h/R)  _________________________ (8)

So as depth h increases, the value of acceleration due to gravity falls.