Two satellites A and B of masses 200 kg and 400 kg are revolving… | JEE Main 2021 (25 Feb, Shift 1)

Q52JEE Main 2021 · 25 FEB · SHIFT 1Difficult

Satellites - Orbital Velocity & Period

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

If TA and TB are the time periods of A and B respectively then the value of TB $-$ TA:

[Given: radius of earth = 6400 km, mass of earth = 6 $\times$ 1024 kg]

Show answer and solution

Answer: (a)

Orbit radii: $r_A = 6400 + 600 = 7000$ km, $r_B = 6400 + 1600 = 8000$ km. $T = 2\pi\sqrt{\frac{r^3}{GM}}$ (mass of satellite does not matter).
$GM = 6.67\times10^{-11}\times6\times10^{24} = 4.0\times10^{14}$ SI
$T_A = 2\pi\sqrt{\frac{3.43\times10^{20}}{4.0\times10^{14}}} \approx 5.82\times10^3$ s, $T_B = 2\pi\sqrt{\frac{5.12\times10^{20}}{4.0\times10^{14}}} \approx 7.11\times10^3$ s
$T_B - T_A \approx 1.3\times10^3$ s
So the answer is (a) $1.33\times10^3$ s.

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