Question

The acceleration due to gravity at a height $2\text{km}$ above the earth surface is same as that of acceleration due to gravity at depth ${}^{\prime }{d}^{\prime }$ below the surface of earth. Then d is equal to

• A. $4\text{km}$
• B. $2\text{km}$
• C. $1\text{km}$
• D. $8\text{km}$

Answer 1

The correct option is A $4\text{km}$

$g_h=g(1-\frac{2h}{R})$ for $h<<R_e$

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

$g(1-\frac{2h}{R})=g(1-\frac{d}{R})$

$\frac{2h}{R}=\frac{d}{R}$

$d=2h=4km$