JEE Advanced 2023 Paper 1 Q07 Physics Gravitation Satellite Motion Easy

JEE Advanced 2023 Paper 1 · Q07 · Satellite Motion

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 $h_P$ and $h_Q$, respectively, where $h_P = R/3$. The accelerations of $P$ and $Q$ due to Earth's gravity are $g_P$ and $g_Q$, respectively. If $g_P/g_Q = 36/25$, what is the value of $h_Q$?

  1. A. $3R/5$
  2. B. $R/6$
  3. C. $6R/5$
  4. D. $5R/6$
Reveal answer + step-by-step solution

Correct answer:A

Solution

$g \propto 1/r^2$, so $g_P/g_Q = (r_Q/r_P)^2 = 36/25 \Rightarrow r_Q/r_P = 6/5$. With $r_P = R + R/3 = 4R/3$: $r_Q = (6/5)(4R/3) = 8R/5$. Thus $h_Q = r_Q - R = 8R/5 - R = 3R/5$.

Want to drill deeper? Open this question inside SolveKar AI and tap "Why?" on any step — the AI Mentor reads your full solution context and explains until it clicks. Download SolveKar AI →