Question

The dependence of acceleration due to gravity on the distance r from the centre of the earth assumed to be a sphere of radius R of uniform density is as shown figure below.

(i) (ii) (iii) (iv)

The correct figure is.

• A. (i)
• A. (ii)
• B. (iii)
• C. (iv)

Answer 1

Answer: (C)

(iv)

Answer 2

The acceleration due to gravity at a depth d below the surface of earth is

$g ^ { \prime } = g \left( 1 - \frac { d } { R } \right) = g \left( \frac { R - d } { R } \right) = g \frac { r } { R }$ ….. (i)

Where R – d = r = distance of locations form the centre of the earth. When r = 0, g` = 0

From (i) g $\propto$r till R = r, for which g` = g

For r > R,

Here, R + h = r

Therefore, the variation of g with distance r from centre of earth will be as shown in figure (4).Thus, options (4) is correct.