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  • Two statellites A and B of masses 200kg and 400kg are revolving round the earth at height of 600km and 1600km respectively. If TA and TB are the time periods of A and B respectively then the value of  TBn

Two statellites A and B of masses 200kg and 400kg are revolving round the earth at height of 600km and 1600km respectively. If TA and TB are the time periods of A and B respectively then the value of  TB -   TA
Option: 1  1.33 x 103 s
Option: 2  3.33 x 102 s
Option: 3  4.24 x 103 s
Option: 4  4.24 x 102 s

Answers (1)

best_answer

\begin{array}{l} \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{r}^{3}}{\mathrm{GM}}} \\ \\ \mathrm{T}_{\mathrm{A}}=2 \pi \sqrt{\frac{((6400+600) \times 10^{3})^3}{\mathrm{GM}}} \\ \\ \mathrm{T}_{\mathrm{A}}=2 \pi \times 10^{9} \sqrt{\frac{7^{3}}{\mathrm{GM}}} \\ \mathrm{T}_{\mathrm{B}}=2 \pi \times 10^{9} \sqrt{\frac{8^{3}}{\mathrm{GM}}} \\ \\ \mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}=\frac{2 \pi* 10^{9}}{\sqrt{\mathrm{GM}}}[8 \sqrt{8}-7 \sqrt{7}]\\ \\\mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}=314 \times 4.107 =1289.64 =1.289 \times 10^{3} \mathrm{~s} \end{array}

So 

T_B-T_A\approx 1.33 \times 10^3 s

Posted by

avinash.dongre

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