Imagine a light planet revolving around a ver | vedclass

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

Question

(B) For a planet of mass $m$ revolving in a circular orbit of radius $R$ with angular velocity $\omega$,the centripetal force is provided by the gravi

Vedclass · Accepted Answer

$T^2 \propto R^{7/2}$

Vedclass · Answer

(B) For a planet of mass $m$ revolving in a circular orbit of radius $R$ with angular velocity $\omega$,the centripetal force is provided by the gravitational force.Given that the gravitational force $F \propto R^{-5/2}$,we can write $F = k R^{-5/2}$ for some constant $k$.The centripetal force is given by $F = m R \omega^2$.Equating the two,we have $m R \omega^2 \propto R^{-5/2}$.Since $\omega = \frac{2\pi}{T}$,we substitute this into the equation: $m R (\frac{2\pi}{T})^2 \propto R^{-5/2}$.This simplifies to $\frac{R}{T^2} \propto R^{-5/2}$.Rearranging for $T^2$,we get $T^2 \propto R \cdot R^{5/2} = R^{1 + 5/2} = R^{7/2}$.Thus,$T^2 \propto R^{7/2}$.

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

Similar Questions

Two satellites are launched simultaneously into orbits of radius $R$ and $4R$. At an instant,the two satellites are on the same radial line. The time after which they have maximum separation is (mass of Earth = $M_e$). Assume the same sense of rotation.

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?

At which height can a satellite be in a geostationary orbit? To remain geostationary,obtain the equation for its height from the surface of the Earth.

The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

Vedclass Test Series

Exam Paper Generator

Online Exam Module