Question

Acceleration due to gravity is maximum at $(R$ is the radius of earth)

• A. a height $\frac{R}{2}$ from the earth's surface
• B. the centre of the earth
• C. the surface of the earth
• D. a depth $\frac{R}{2}$ from earth's surface

Answer 1

Answer: (C)

Acceleration due to gravity at a height $h$ above the earth's surface is
$g_h=\frac{g}{{\left(1+\frac{h}{R}\right)}^2}$
where $g$ is the acceleration due to gravity on the earth's surface.
At $h=\frac{R}{2},g_h=\frac{g}{{\left(1+\frac{R}{2R}\right)}^2}=\frac{4g}{9}$
Acceleration due to gravity at a depth $d$ below the earth's surface is
$g_d=g\left(1-\frac{d}{R}\right)$
At $d=\frac{R}{2},g_d=g\left(1-\frac{R}{2R}\right)=\frac{g}{2}$
At the centre of earth, $d=R,g_d=g\left(1-\frac{R}{R}\right)=0$ Thus, the acceleration due to gravity is maximum on the earth's surface.