A small planet is revolving around a very mas | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For a planet to orbit a star in a circular path,the gravitational force provides the necessary centripetal force.Given that the gravitational forc

Vedclass · Accepted Answer

$R^{7/4}$

Vedclass · Answer

(D) For a planet to orbit a star in a circular path,the gravitational force provides the necessary centripetal force.Given that the gravitational force $F_G \propto R^{-5/2}$.The centripetal force is given by $F_c = m \omega^2 R$,where $\omega = \frac{2\pi}{T}$.Thus,$F_c = m \left(\frac{4\pi^2}{T^2}\right) R$.Equating the forces: $m \left(\frac{4\pi^2}{T^2}\right) R \propto R^{-5/2}$.Since $m$ and $4\pi^2$ are constants,we have $\frac{R}{T^2} \propto R^{-5/2}$.Rearranging for $T^2$: $T^2 \propto R \cdot R^{5/2} = R^{7/2}$.Taking the square root on both sides: $T \propto R^{7/4}$.

$A$ small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force between the planet and the star were proportional to $R^{-5/2}$,then $T$ would be proportional to:

Similar Questions

The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as

Who decides the upward direction in an artificial satellite?

Two satellites of masses $m$ and $4m$ are revolving in the same orbit around the Earth. Which one of the following statements is correct?

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

Earth revolves around the sun in a circular orbit of radius $R$. The angular momentum of the revolving Earth is directly proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module