Home
Class 11
PHYSICS
Imagine a light planet revolving around ...

Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. On what power of r will the square of time period will depend if the gravitational force of attraction between the planet and the star is proportional to `r^(-5//2)`.

Text Solution

Verified by Experts

The resultant gravitational force provides necessary centripetal force `(mV^2)/r=(K)/(r^(5//2))impliesV^(2)=K/(mr^(3//2))`
So that `T = (2pir)/V=2pirsqrt(("mr"^(3//2))/K)`
So `T^(2) prop r^(7//2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

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 proportational to R^(-5//2) , then (a) T^(2) is proportional to R^(2) (b) T^(2) is proportional to R^(7//2) (c) T^(2) is proportional to R^(3//3) (d) T^(2) is proportional to R^(3.75) .

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 proportational to R^(-5//2) , then (a) T^(2) is proportional to R^(2) (b) T^(2) is proportional to R^(7//2) (c) T^(2) is proportional to R^(3//3) (d) T^(2) is proportional to R^(3.75) .

Imagine a light planet revolving around a massive star in a circular orbit of raidus r with a a period of revolution T. If the gravitational force of attraction between planet and the star is proportioanl to r^(-5)//^(2) , then find the relation between T and r.

If a planet revolves around the sun in a circular orbit of radius a with a speed of revolution T, then (K being a positive constant

A small planet is revolving around a 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

A planet is revolving around the sun in a circular orbit with a radius r. The time period is T .If the force between the planet and star is proportional to r^(-3//2) then the quare of time period is proportional to

The period of revolution of a satellite in an orbit of radius 2R is T. What will be its period of revolution in an orbit of radius 8R ?

Two satellites of masses M and 16 M are orbiting a planet in a circular orbitl of radius R. Their time periods of revolution will be in the ratio of

Consider a planet moving around a star in an elliptical orbit with period T. Area of elliptical orbit is proportional to

The period of a satellite in a circular orbit of radius R is T. What is the period of another satellite in a circular orbit of radius 4 R ?