Home
Class 12
PHYSICS
if velocity given to an object from the ...

if velocity given to an object from the surface of the earth is n times the escapes velocity then what will be the residual velocity at inifinity.

Text Solution

Verified by Experts

Let residual velocity be v then from energy conservation `(1)/(2)m(nv_(e))^(2)-(GMm)/(R)=(1)/(2)mv^(2)+0`
`impliesv^(2)=n^(2)v_(e)^(2)-(2GM)/(R)=n^(2)v_(e)^(2)-v_(e)^(2)-v_(e)^(2)=(n^(2)-1)v_(e)^(2)impliesv=(sqrt(n^(2)-1))v_(e)`
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    ALLEN|Exercise Exercise 1 (Check your Grasp)|28 Videos

  • GRAVITATION

    ALLEN|Exercise Exercise 2 (Brain Teasers)|27 Videos

  • GEOMETRICAL OPTICS

    ALLEN|Exercise subjective|14 Videos

  • KINEMATICS-2D

    ALLEN|Exercise Exercise (O-2)|48 Videos

Similar Questions

Explore conceptually related problems

Escape velocity on the earth

The escape velocity of a body from the surface of the earth is equal to

The escape velocity of a body from the surface of earth is

The escape velocity of a rocket launched from the surface of the earth

A body is projected from the surface of the earth with thrice the escape velocity (V_(e)) from the surface of the earth. What will be its velocity, when it will escape the gravitational pull?

The escape velocity from the surface of the earth is (where R_(E) is the radius of the earth )

An objects is projected vertically upwards from the surface of the earth with a velocity 3 times the escape velocity v_(e ) from earth's surface. What will be its final velocity after escape from the earth's gravitational pull ?

Statement I : Escape velocity of a tennis ball from the surface of earth is the same as the escape velocity of a cricket ball from the surface of earth. Statement II : Escape velocity of a body is independent of the mass of the body