JEE Advanced 2023 · Paper 1 · Physics Q7

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PhysicsSingle correct+3 / -1Question 24 of 51

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 $h_Q$ ?

3R/5

R/6

6R/5

5R/6

Answer and worked solution

Official answer: A

Since $g=\dfrac{GM}{(R+h)^2}$ :
$\frac{g_P}{g_Q}=\frac{(R+h_Q)^2}{(R+h_P)^2}=\frac{36}{25}\implies\frac{R+h_Q}{4R/3}=\frac65.$

So $R+h_Q=\frac{8R}{5}$ and $h_Q=\frac{3R}{5}$ .

Topics:Variation of g Satellites and orbital motion

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JEE Advanced 2023 · Paper 1, Physics question 7