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JEE Main 202125 FebruaryMorning Shift

Exam: JEE Main
Year: 2021
Date: 25 February
Shift: Morning Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2021 · 25 February · Morning Shift · Physics · Gravitation

Two satellites A and B of masses 200kg and 400kg are revolving...

Two satellites

A

and

B

of masses

200kg

and

400kg

are revolving round the earth at height of

600km

and

1600km

respectively. If

{T}_{A}

and

{T}_{B}

are the time periods of

A

and

B

respectively then the value of

{T}_{B} - {T}_{A}

:

Two satellites A and B of masses 200kg and 400kg are revolving round the earth at height of 600km and 1600km

[ Given : radius of earth $= 6400km,$ mass of earth $= 6 \times {10}^{24}kg$ ]

Options

A $4 . 24 \times {10}^{3}s$
B $3 . 33 \times {10}^{2}s$
C $1 . 33 \times {10}^{3}s$
D $4 . 24 \times {10}^{2}s$

Correct answer

C. $1 . 33 \times {10}^{3}s$

Step-by-step solution

$⇒ T = 2\pi\sqrt{\dfrac{{r}^{3}}{GM}}$

$⇒ {T}_{A} = 2\pi\sqrt{\dfrac{\left(6400 + 600\right) \times {10}^{3}}{GM}}$

$⇒ {T}_{B} = 2\pi \times {10}^{9}\sqrt{\dfrac{{8}^{3}}{GM}}$

$⇒ {T}_{B} - {T}_{A} = \dfrac{2\pi{10}^{9}}{\sqrt{GM}}\left[8\sqrt{8} - 7\sqrt{7}\right]$

$= 314 \times 4 . 107$

$= 1289 . 64$

$= 1 . 289 \times {10}^{3}s$

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