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

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

Tardigrade Admin · Accepted Answer

Time period of a satellite is the time taken by satellite to go once around the earth.

T = 2 π \frac{r ^{3}}{MG}

,
so

T

depends on

r^{\frac{3}{2}}

.
so if

r

is increased to

4

times then time period will be

8

times

(4^{\frac{3}{2}} = 8)

.

Q. 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

10 hours

80 hours

40 hours

20 hours

Time period of a satellite is the time taken by satellite to go once around the earth. T=2πMGr3​​, so T depends on r23​. so if r is increased to 4 times then time period will be 8 times (423​=8).

Q. 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

Time period of a satellite is the time taken by satellite to go once around the earth. $T = 2 π \frac{r ^{3}}{MG}$ ,
so $T$ depends on $r^{\frac{3}{2}}$ .
so if $r$ is increased to $4$ times then time period will be $8$ times
$(4^{\frac{3}{2}} = 8)$ .