Home
Class 11
PHYSICS
Show that the critical velocity of a bod...

Show that the critical velocity of a body revolving in a circular orbit very close to the surface of a planet of radius R and mean density `rho` is `2R sqrt((Gpi rho)/(3))` .

Text Solution

Verified by Experts

Since the body is revolving very close to the planet, h = 0
`rho = M/V = (M)/(4/3 pi R^3)`
` therefore M = 4/3 pi R^3 rho`
Critical velocity
`v_c = sqrt((GM)/(R )) = sqrt((G 4/3 pi R^3 rho) /(R ))`
` therefore v_c = 2R sqrt((G pi rho)/(3))`
When a satellite revolves very close to the surface of the Earth, motion of satellite gets affected by the friction produced due to resistance of air. In deriving the above expression the resistance of air is not considered.
Promotional Banner

Similar Questions

Explore conceptually related problems

The gravitational acceleration on the surface of earth of radius R and mean density rho is

The escape velocity from the surface of the earth of radius R and density rho

Show that the escape velocity of a body from the surface of a planet of radius R and mean density rho is Rfrac(sqrt8pirhoG)(3) OR Show that the escape velocity of a body from the surface of the earth is 2Rfrac(sqrt2pirhoG)(3) , where R is the radius of the earth and rho is the mean density of the earth. OR Obtain formula of escape velocity of a body at rest on the earth's surface in terms of mean density of erth.

A satellite is revolving in a circular orbit very close to the surface of earth. Find the period of revolution of the satellite

Escape velocity of a body from the surface of a spherical planet of mass M, radius R and density p is

The centr of mass of a right circular coneof height h, radius R and constant density rho is at

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3.

The orbital velocity of a body at height h above the surface of Earth is 36% of that near the surface of the Earth of radius R. If the escape velocity at the surface of Earth is 11.2 km s^-1 , then its value at the height h will be

A satelite is revolving in a circular orbit at a height h above the surface of the earth of radius R. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between h and R is