Home
Class 11
PHYSICS
The minimum velocity of projection of a ...

The minimum velocity of projection of a body to send it to infinity from the surface of a planet is `(1)/(sqrt(6))` times that is required from the surface of the earth. The radius of the planet is `(1)/(36)` times the radius of the earth. The planet is surrounded by an atmosphere which contains monoatomic innert gas `(gamma = 5//3)` of constant density up to a height h(`h lt lt` radius of the planet). Find the velocity of sound on the surface of the planet.

Text Solution

Verified by Experts

Escape velocity from the surface of the planet
`v_(p)=sqrt(2g_(p)R_(p))`
Given `v_(p)=(v_(e ))/(sqrt(6)) = sqrt((2g_(e )R_(e ))/(6))`
`sqrt((g_(e )R_(e ))/(3)) = sqrt(2g_(p)R_(e )//36) rArr g_(p) =6g_(e )`
Pressure exerted by the atmospheric column of height h on the surface of the planet `P = rho g_(P) h`
Using equation of state `P = (rho RT)/(M)`
Hence speed of the sound `v = sqrt((yRT)/(M)) = sqrt(yg_(p)h) = sqrt(6y g_(e )h) = sqrt(10 g_(e )h)`
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    BANSAL|Exercise Solved Example|8 Videos

  • GRAVITATION

    BANSAL|Exercise Practice Exercise|18 Videos

  • CENTRE OF MASS & MOMENTUM CONSERVATION

    BANSAL|Exercise EXERCISE-4 (SECTION-B) (JEE-ADVANCED Previous Year Questions)|8 Videos

  • HEAT TRANSFER

    BANSAL|Exercise Exercise|89 Videos

Similar Questions

Explore conceptually related problems

The radius of orbit of a planet is two times that of the earth. The time period of planet is

A body projected from the surface of the earth attains a height equal to the radius of the earth. The velocity with which the body was projected is

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R , the radius of the planet would be

If the radius of a planet is four times that of earth and the value of g is same for both, the escape velocity on the planet will be

If the radius of a planet is four times that of earth and the value of g is same for both, the escape velocity on the planet will be

The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth be R, then radius of the planet would be

The escape velocity from the surface of the earth is V_(e) . The escape velcotiy from the surface of a planet whose mass and radius are three times those of the earth, will be