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  4. 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 T A and T B are the time periods of A and B respectively then the value of T B - T A <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/2133691a9c04376dac0a63973ebb9436-.png /> [Given: radius of earth =6400 km, mass of earth .=6 × 1024 kg ]

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Q. 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 $T _{ A }$ and $T _{ B }$ are the time periods of $A$ and $B$ respectively then the value of $T _{ B }- T _{ A }$
image
[Given : radius of earth $=6400 km$, mass of earth $\left.=6 \times 10^{24} kg \right]$

JEE MainJEE Main 2021Gravitation

Solution:

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