Physics · Gravitation

JEE Advanced 2023 — Paper 1 — Question 23

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 $h_{Q}$ ?

Option A:
$3 \mathrm{R} / 5$
Correct
Option B:
$\mathrm{R} / 6$
Option C:
$6 R / 5$
Option D:
$5 R / 6$

Answer: A

Step-by-step solution

\begin{aligned} & g_{P}=\frac{G M}{\left(\mathrm{R}+\frac{\mathrm{R}}{3}\right)^{2}} \\ & \mathrm{~g}_{\mathrm{Q}}=\frac{\mathrm{GM}}{\left(\mathrm{R}+\mathrm{h}_{\mathrm{Q}}\right)^{2}} \\ & \frac{36}{25}=\frac{\mathrm{g}_{\mathrm{P}}}{\mathrm{~g}_{\mathrm{Q}}} \Rightarrow \sqrt{\frac{36}{25}}=\frac{\mathrm{R}+\mathrm{h}_{\mathrm{Q}}}{\frac{4 \mathrm{R}}{3}} \\ & \Rightarrow\left(\frac{4 \mathrm{R}}{3}\right) \cdot\left(\frac{6}{5}\right)=\mathrm{R}+\mathrm{h}_{\mathrm{Q}} \\ & \Rightarrow \mathrm{~h}_{\mathrm{Q}}=\frac{3 \mathrm{R}}{5} \end{aligned}

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2023
Paper: Paper 1
Subject: Physics
Chapter: Gravitation
Topic: Gravitational Field and Gravity