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The velocity with which a projectile mus...

The velocity with which a projectile must be fired so that is escapes earth's gravitation does not depend on:

A

Mass of the earth

B

Mass of the projectile

C

Radius of the projectile's orbit

D

Gravitational constant.

Text Solution

Verified by Experts

The correct Answer is:
B
For a projectile to leave the gravitational field of the earth, its kinetic energy would be at least equal to potential energy. That is
`1/2mv_e^2=G(Mm)/(R) rArr v_e= sqrt((2GM)/(R))`
Where G is the universal gravitational constant, M is the mass of the earth and R is the radius of the earth. hence the escape velocity of a projectile is independent of its own mass
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Knowledge Check

  • The velocity with which a projectile must be fired so that it escape earth's gravitational does not depend on

    A
    mass of the earth
    B
    radius of the projectile's orbit
    C
    mass of the projectile
    D
    gravitational constant

  • The velocity with which a projectile must be fired to escape from the earth does not depend upon

    A
    mass of earth
    B
    mass of projectile
    C
    radius of earth
    D
    None of these

  • The escape velocity does not depend upon

    A
    mass of the body,
    B
    height of the location from where it is projected
    C
    density of the body,
    D
    None of these.

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