JEE MAIN - Physics (2021 - 25th February Morning Shift - No. 7)
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 :
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[Given : radius of earth = 6400 km, mass of earth = 6 $$\times$$ 1024 kg]
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]
1.33 $$\times$$ 103 s
4.24 $$\times$$ 102 s
3.33 $$\times$$ 102 s
4.24 $$\times$$ 103 s
Explanation
$$T = 2\pi \sqrt {{{{r^3}} \over {GM}}} $$
$${T_A} = 2\pi \sqrt {{{{{\left( {6400 + 600} \right)}^3}} \over {GM}}} $$
$${T_A} = 2\pi \times {10^9}\sqrt {{{{7^3}} \over {GM}}} $$
$${T_B} = 2\pi \times {10^9}\sqrt {{{{8^3}} \over {GM}}} $$
$${T_B} - {T_A} = {{2\pi {{10}^9}} \over {\sqrt {GM} }}\left[ {8\sqrt 8 - 7\sqrt 7 } \right]$$
$$ = 314 \times 4.107$$
$$ = 1289.64$$
$$ = 1.289 \times {10^3}s$$
$${T_A} = 2\pi \sqrt {{{{{\left( {6400 + 600} \right)}^3}} \over {GM}}} $$
$${T_A} = 2\pi \times {10^9}\sqrt {{{{7^3}} \over {GM}}} $$
$${T_B} = 2\pi \times {10^9}\sqrt {{{{8^3}} \over {GM}}} $$
$${T_B} - {T_A} = {{2\pi {{10}^9}} \over {\sqrt {GM} }}\left[ {8\sqrt 8 - 7\sqrt 7 } \right]$$
$$ = 314 \times 4.107$$
$$ = 1289.64$$
$$ = 1.289 \times {10^3}s$$
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