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:

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10 hours

80 hours

40 hours

20 hours

answer is C.

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Detailed Solution

Concept: In this question, we will discuss the relation of time period wrt. distance of satellite and earth.
Given,
Time period of satellite = 5 hours
So, velocity of satellite will be given by:

…………..(i)
Where, G is the universal gravitational constant, M is the mass of earth and R is the radius of the orbit of the satellite.
Now, we know that velocity can also be given by:

………………….(ii)
where T is the satellite's orbital period.
So, by equating (i) and (ii) ,
Question Image

Now, taking R as the radius when T1= 5 hours

………(iii)
Also, T2 as the radius when R is four times the old R

………..(iv)
Now, dividing (iv) by (iii) ,
Question Image

So, the time period after increasing the radius by 4 times is 40 hours.
Hence, the correct option is 3.

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