JEE PYQ: Gravitation Question 13
Question 13 - 2021 (25 Feb Shift 1)
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 $T_B - T_A$:
[Given: radius of earth = 6400 km, mass of earth $= 6 \times 10^{24}$ kg]
(1) $4.24 \times 10^2$ s
(2) $3.33 \times 10^2$ s
(3) $1.33 \times 10^3$ s
(4) $4.24 \times 10^3$ s
Show Answer
Answer: (3)
Solution
$T = 2\pi\sqrt{\frac{r^3}{GM_e}}$. For A: $r_A = 7000$ km. For B: $r_B = 8000$ km. $T_B - T_A = 2\pi\left(\sqrt{\frac{(8000 \times 10^3)^3}{G \times 6 \times 10^{24}}} - \sqrt{\frac{(7000 \times 10^3)^3}{G \times 6 \times 10^{24}}}\right) \approx 1.33 \times 10^3$ s.
BETA
