Question

State whether true or false.

The value of acceleration due to gravity becomes half at a depth of half the radius of the earth.

• A. True
• B. False

Answer 1

The correct option is A True

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

Let 'p' be the density of the material of earth

mass = volume * density

M=$\frac{4}{3}\pi R^{3}p$

Substituting in eq 1 we get

$g=\frac{G}{R^2}\ast \frac{4}{3}\pi R^{3}p=\frac{4}{3}\pi GRp$ - eq. 2

Now at depth 'd'

$g_d=\frac{4}{3}\pi G(R-d)p$

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

if d=R/2

then $g_d=g(1-\frac{R}{2R})=g(1-\frac{1}{2})=\frac{1}{2}g$

Thus value of acceleration due to gravity at a depth of half of the radius of the earth.