Question

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 $T_B-T_A$

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

• A. $1.33\times 10^{3}s$
• B. $3.33\times 10^{2}s$
• C. $4.24\times 10^{3}s$
• D. $4.24\times 10^{2}s$

Answer 1

Answer: (A)

$T=2\pi \sqrt{\frac{r^3}{GM}}$
$T_A=2\pi \sqrt{\frac{(6400+600)\times 10^3}{GM}}$
$T_A=2\pi \times 10^9\sqrt{\frac{7^3}{GM}}$
$T_B=2\pi \times 10^9\sqrt{\frac{8^3}{GM}}$
$T_B-T_A=\frac{2\pi 10^9}{\sqrt{GM}}[8\sqrt{8}-7\sqrt{7}]$
$=314\times 4.107$
$=1289.64$
$=1.289\times 10^{3}s$