Question

The acceleration due to gravity at a height ${\left(\frac{1}{20}\right)}^{th}$ the radius of earth above earth's surface is $9m/s^2$. Its value at a point at an equal distance below the surface of earth is ________ $m/s^2$.

• A. $55m/s^2$
• B. $9.5m/s^2$
• C. $12m/s^2$
• D. $15m/s^2$

Answer 1

The correct option is B $9.5m/s^2$

The variation of acceleration due to gravity outside the earth.

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

$g^1=g(1-\frac{1}{10})$

$g=g\left(\frac{9}{10}\right)$

$g=10m/s^2$

Now, for inside point,

$g^{11}=g(1-\frac{d}{R})$

$g^{11}=10(1-\frac{1}{20})$

$g^{11}=9.5m/s^2$