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JEE Main 202329 JanuaryEvening Shift
Exam
JEE Main
Year
2023
Date
29 January
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2023 · 29 January · Evening Shift · Physics · Gravitation

The time period of a satellite of earth is 24 hours. If the...

The time period of a satellite of earth is 2424 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

Options

  1. A44 hours
  2. B66 hours
  3. C1212 hours
  4. D33 hours

Correct answer

D. 33 hours

Step-by-step solution

From Kepler's law of periods, we know

T2∝R3{T}^{2} ∝ {R}^{3}

⇒T12T22=R13R23⇒(T1T2)2=(RR4)3⇒ {T}_{1}^{2}{T}_{2}^{2} = {R}_{1}^{3}{R}_{2}^{3} ⇒ {\left(\dfrac{{T}_{1}}{{T}_{2}}\right)}^{2} = {\left(\dfrac{R}{\dfrac{R}{4}}\right)}^{3}

⇒T12T22=64⇒ {T}_{1}^{2}{T}_{2}^{2} = 64

∴T2=248=3∴ {T}_{2} = \dfrac{24}{8} = 3 hours

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