Question

The depth at which the value of $g$ becomes $25\%$ of that at the surface of the earth. $($ Radius of the earth $=$ 6400km.$)$

• A. 4800 km
• B. 2400 km
• C. 3600 km
• D. 1200 km

Answer 1

The correct option is A 4800 km

The value of $g$ at a depth is given by:
$g_d=g(1-\frac{d}{R})$

Here, $g_d=\frac{g}{4}$
$\Rightarrow \frac{g}{4}=g(1-\frac{d}{R})$
$\Rightarrow \frac{d}{R}=\frac{3}{4}$
$\Rightarrow d=0.75\times 6400=4800km$