Question

At what height above the earth's surface does the value of g becomes 36% of the value at the surface of earth ?

• A. $\frac{2R}{5}$
• B. $\frac{2R}{3}$
• C. $\frac{3R}{7}$
• D. $\frac{R}{3}$

Answer 1

Answer: (B)

$\frac{2R}{3}$

We have,

$\begin{array}{c}\frac{GM}{{\left(R+h\right)}^2}=\frac{36}{100}\frac{Gm}{R^2}\\ \Rightarrow 100R^2=36{\left(R+h\right)}^2\\ \Rightarrow 25R^2=9\left(R^2+h^2+2Rh\right)\\ \Rightarrow 25R^2=9R^2+9h^2+18Rh\\ \Rightarrow 16R^2=9h^2+18Rh\\ \Rightarrow 9h^2+18Rh-16R^2=0\\ R=\frac{-18+\sqrt{324+576}}{18}R\\ =\frac{-18+30}{18}R\\ =\frac{12R}{18}=\frac{2R}{3}\\ h=\frac{2R}{3}\end{array}$

Then,

Option $B$ is correct answer.