Answer
398.4k+ views
Hint:Here given that the satellite is revolving on a circular radius around the earth having a radius of $4R$, hence to find the time period of the satellite in which it completes its revolution the concept of Kepler’s law is used. Here the Kepler’s third law should be used to evaluate the time period of the satellite.
Complete step by step answer:
As discussed this question can be solved and the time period can be evaluated by using Kepler’s third law. Kepler’s third law states that the square of the time period given as ${T^2}$ of the revolution of the planet around the sun is directly proportional to the cube of the semi-major axis of the orbit that is the radius of the orbit of the planet which can be assumed as circular. Hence the relation between the time period of the planet $T$ and the radius $R$ of the orbit of the revolution of the planet can be given as
$\begin{array}{*{20}{c}}
{{T^2}}& \propto &{{R^3}}
\end{array}$ ……….. $(1)$
Now as it is given that the radius becomes $4R$ which is four times from the radius of another satellite hence substituting this in equation $(1)$ results in
$\begin{array}{*{20}{c}}
{{T^2}}& \propto &{{{\left( {4R} \right)}^3}}
\end{array}$
$\begin{array}{*{20}{c}}
{ \Rightarrow {T^2}}& \propto &{64{R^3}}
\end{array}$
On comparing the values on both sides as the square of the time period is proportional to the cube of the radius. Therefore the time period would be given as
$\begin{array}{*{20}{c}}
{64{T^2}}& \propto &{64{R^3}}
\end{array}$
$\begin{array}{*{20}{c}}
{ \Rightarrow {{\left( {8T} \right)}^2}}& \propto &{{{\left( {4R} \right)}^3}}
\end{array}$
Hence the time period of the satellite when the radius of the orbit becomes $4R$ is given $8T$.
Therefore option C is the correct answer.
Note:There are three Kepler's law that governs the planetary motions. The first Kepler's law states that the planets move around the sun in an elliptical orbit. The second law states that planets move around the sun as its foci and the third law as we had already discussed which is used to evaluate the time period of the satellite for the given radius.
Complete step by step answer:
As discussed this question can be solved and the time period can be evaluated by using Kepler’s third law. Kepler’s third law states that the square of the time period given as ${T^2}$ of the revolution of the planet around the sun is directly proportional to the cube of the semi-major axis of the orbit that is the radius of the orbit of the planet which can be assumed as circular. Hence the relation between the time period of the planet $T$ and the radius $R$ of the orbit of the revolution of the planet can be given as
$\begin{array}{*{20}{c}}
{{T^2}}& \propto &{{R^3}}
\end{array}$ ……….. $(1)$
Now as it is given that the radius becomes $4R$ which is four times from the radius of another satellite hence substituting this in equation $(1)$ results in
$\begin{array}{*{20}{c}}
{{T^2}}& \propto &{{{\left( {4R} \right)}^3}}
\end{array}$
$\begin{array}{*{20}{c}}
{ \Rightarrow {T^2}}& \propto &{64{R^3}}
\end{array}$
On comparing the values on both sides as the square of the time period is proportional to the cube of the radius. Therefore the time period would be given as
$\begin{array}{*{20}{c}}
{64{T^2}}& \propto &{64{R^3}}
\end{array}$
$\begin{array}{*{20}{c}}
{ \Rightarrow {{\left( {8T} \right)}^2}}& \propto &{{{\left( {4R} \right)}^3}}
\end{array}$
Hence the time period of the satellite when the radius of the orbit becomes $4R$ is given $8T$.
Therefore option C is the correct answer.
Note:There are three Kepler's law that governs the planetary motions. The first Kepler's law states that the planets move around the sun in an elliptical orbit. The second law states that planets move around the sun as its foci and the third law as we had already discussed which is used to evaluate the time period of the satellite for the given radius.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)