Question

The time period of a satellite of earth is 5 hours. If the
separation between the earth and the satellite is increased
to 4 times the previous value, the new time period will become
(a) 10 hours
(b) 80 hours
(c) 40 hours
(d) 20 hours​

Answer 1

Answer:

option (c) I hope your problem is solved plz give response with thanked and mark as brainliest

Answer 2

$\underbrace{\bf\:Solution}$

❍ Concept:-

Law of period :- The square of time taken by the planet to revolve around the sun is directly proportional to the cube of mean distance.

$\rm\:{T}^{2}\propto\:{r}^{3}$

Now,

⠀ ⠀ ⠀⠀⠀ ⠀ ⠀⠀ ⠀ $\rm\:r_1$

$\rm\:E\:\rule{150}1\:{S}$

$\rm\:{T_1}^{2}={kr_1}^{3}$

$\rm\:{(5)}^{2}={kr_1}^{3}$

$\rm\:{kr_1}^{3}=25\:..............(i)$

⠀ ⠀ ⠀⠀⠀ ⠀ ⠀⠀ $\rm\:r_2=4r_1$

$\rm\:E\:\rule{150}1\:{S}$

$\rm\:{T}^{2}={kr_2}^{3}$

$\rm\:{T}^{2}=k(4r_1)^3$

$\rm\:{T}^{2}=k\:64\:{r_1}^{3}$

$\rm\:{T}^{2}=64\:k{r_1}^{3}$

$\rm\:{T}^{2}=64\times\:25\:\:\:\:\:[25\:from\:eq(i)]$

$\rm\:T=\sqrt{64\times\:25}$

$\rm\:T=8\times\:5$

$\rm\:T=40\:hours$

Hence,the new time period will becomes 40 hours.

so, option (c) 40 hours is correct answer.