Question

The time period of a satellite of earth is $5h$. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become:

• A. $10h$
• B. $80h$
• C. $40h$
  
• D. $20h$
  

Answer 1

Answer: (C)

$40h$

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

$T=2\pi \sqrt{\frac{r^3}{MG}}$,

so T depends on $r^{\frac{3}{2}}$.

so if r is increased to 4 times then time period will be 8 times ($4^{\frac{3}{2}}=8$).

so beat answer is option c.