Question

The Ratio of gravity field due to the earth at high hP and hQ from the earth's surface is $\frac{g_{P}}{g_{Q}}=\frac{36}{25}.$ If $h_P=\frac{R}{2}$, then the value of hQ will be

• A. $\frac{3R}{4}$
• B. $\frac{3R}{5}$
• C. $\frac{4R}{5}$
• D. $\frac{5R}{6}$

Answer 1

Answer: (C)

$\frac{4R}{5}$

Answer 2

The correct answer is option(C).
$\frac{g_P}{g_Q}=\frac{\frac{GM}{r_p^2}}{\frac{GM}{r_q^2}}=\frac{36}{25}$
$\frac{r_Q}{r_P}=\frac{6}{5}$ $\Rightarrow$ $r_Q=(\frac{6}{5})(\frac{3R}{2})=\frac{9R}{5}$
$h_Q=\frac{9R}{5}-R=\frac{4R}{5}$