Two satellites P and Q are moving in different circular orbits around the Earth (radius 𝑅). The heights of P and Q from the Earth surface are ℎP and ℎQ, respectively, where ℎP = 𝑅/3. The accelerations of P and Q due to Earth’s gravity are 𝑔P and 𝑔Q, respectively. If 𝑔P/𝑔Q = 36/25, what is the value of ℎQ? (A) 3𝑅/5 (B) 𝑅/6 (C) 6𝑅/5 (D) 5𝑅/6

 Given two satellites P and Q moving in circular orbits around the Earth, we need to find the height 

$h_Q$ of satellite Q from the Earth's surface. The height of satellite P is $h_P=\frac{R}{3}$, where $R$ is the Earth's radius. The accelerations due to Earth's gravity for P and Q are $g_P$ and $g_Q$ respectively, with the ratio $\frac{g_P}{g_Q}=\frac{36}{25}$.

1. Determine the orbital radius of satellite P:

   $$r_P=R+h_P=R+\frac{R}{3}=\frac{4R}{3}$$

2. Relate the accelerations using Newton's law of gravitation:

   $$\frac{g_P}{g_Q}={\left(\frac{r_Q}{r_P}\right)}^2$$

   Given $\frac{g_P}{g_Q}=\frac{36}{25}$, we have:

   $${\left(\frac{r_Q}{r_P}\right)}^2=\frac{36}{25}⟹\frac{r_Q}{r_P}=\frac{6}{5}$$

3. Calculate the orbital radius of satellite Q:

   $$r_Q=\frac{6}{5}\times r_P=\frac{6}{5}\times \frac{4R}{3}=\frac{24R}{15}=\frac{8R}{5}$$

4. Determine the height $h_Q$:

   $$h_Q=r_Q-R=\frac{8R}{5}-R=\frac{8R}{5}-\frac{5R}{5}=\frac{3R}{5}$$

Thus, the value of $h_Q$ is $\boxed{{\displaystyle A}}$.