Question

At what depth from the surface of the earth, acceleration due to gravity will be 1/4th the value of g on the surface of the earth?

• A. 0.80 R
• B. 0.75 R
• C. 1.00 R
• D. 0.50 R

Answer 1

The correct option is B 0.75 R

Acceleration due to gravity at depth d inside the earth is:
$g_d=g(1-\frac{d}{R})$
According to the question
$\Rightarrow g_d=\frac{g}{4}$
$\Rightarrow \frac{g}{4}=4(1-\frac{d}{R})$
$\Rightarrow \frac{1}{4}=1-\frac{d}{R}\Rightarrow \frac{d}{R}=\frac{3}{4}$
$\Rightarrow d=\frac{3}{4}\times R=0.75R$