Question

Obtain expression for escape velocity ?

Answer 1

Heya.........!!!!

It is the minimum Velocity with which a body should be projected from the surface of the planet so as to reach infinity .

DERIVATION :

If a body of mass m is projected with velocity Ve from surface of planet mass M and Radius R , So by law of Conservation of Mechanical Energy

KE + PE at surface of planet = KE + PE at infinity .
1/2 ×m×v^2 + ( - GMm/R ) = 0 + 0

1/2 m×v^2 = GMm/R
Or
Ve = √GM/√R
we know that GM = gR^2

so,,
$ve = \sqrt{2gr}$
here r = R only .
If we put value of R and g of Earth we get Ve = 11.2 Km/s ( approx ) .


HOPE IT HELPS U ^_^

Answer 2

Heya,
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An object can be thrown up with a certain minimum initial velocity so that, the object goes beyond the earth's gravitational field and escape from earth, this velocity is known as escape velocity of the earth. So, escape velocity is defined as the minimum initial velocity that will take a body away above the surface of a planet when it's projected vertically upwards.

On throwing the object upwards, work has to be done against the gravity. If a certain minimum velocity is given to an object, such that the work done against gravity from the planet's surface to infinity(outside gravitational field of planet) is equal to the kinetic energy of the object, then it will not return back to the planet.

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The escape velocity is the minimum velocity required to leave a planet or moon. For a rocket or other object to leave a planet, it must overcome the pull of gravity. The formula for escape velocity contains a constant, G, which is called the "universal gravitational constant". Its value is  . The unit for escape velocity is meters per second (m/s).

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