Question

The height at which the value of acceleration due to gravity becomes $50\%$ of that at the surface of the earth$.$ (radius of the earth =$6400km$) is

• A. $2650$
• B. $2430$
• C. $2250$
• D. $2350$

Answer 1

The correct option is A $2650$

Given,

$R=6400km$

$g^{\prime }=50g$%

$g^{\prime }=0.5g$

New gravity at height $h$ is given by

$g^{\prime }=\frac{g{R}^2}{(R+h{)}^2}$

$0.5g=\frac{g{R}^2}{(R+h{)}^2}$

$\frac{(R+h{)}^2}{R^2}=2$

$\frac{R+h}{R}=\sqrt{2}=1.4142$

$1+\frac{h}{R}=1.4142$

$\frac{h}{R}=0.4142$

$h=0.4142R=0.4142\times 6400$

$h=2650km$

The correct option is A.