Physics - Gravitation Question with Solution | TestHub

Acceleration due to gravity at height $h$ is given by $g_h=g{\left(\frac{R}{R+h}\right)}^2$.

Given that $g$ is reduced by $64\%$, the new value is $g_h=g-0.64g=0.36g$.

Equating the two expressions for $g_h$:

$0.36g=g{\left(\frac{R}{R+h}\right)}^2$

$\frac{36}{100}={\left(\frac{R}{R+h}\right)}^2$

Taking the square root on both sides:

$\frac{6}{10}=\frac{R}{R+h}$

$\frac{3}{5}=\frac{R}{R+h}$

$3R+3h=5R$

$3h=2R$

$h=\frac{2}{3}R$

Answer: $\frac{2}{3}R$