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Define escape velocity. Derive an expres...

Define escape velocity. Derive an expression for escape velocity.

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Define escape velocity.Deduce anexpression for the escape velocity and time period of a body that moves in a circular orbit near the earth's surface.

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Knowledge Check

  • The ratio of escape velocity at earth (v_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is

    A
    `1:2 sqrt(2)`
    B
    `1:4`
    C
    `1:sqrt(2)`
    D
    `1:2`

  • This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: There is no gas in the atmosphere of moon. Statement - II: Root mean square velocity of gases are greater than escape velocity of moon.

    A
    Statement - I is true, Statement - II is true, Statement - II is a correct explanation of Statement -I
    B
    Statement - I is true, Statement - II is true, Statement - II is not a correct explanation of Statement -I.
    C
    Statement -I is true, Statement - II is false.
    D
    Statement -I is false, Statement - II is true.

  • The escape velocity of a particle of mass m is

    A
    directly proportional to `m^2`
    B
    directly proportional to m
    C
    directly proportional to `m^0`
    D
    directly proportional to `m^(-1)`

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    Define orbital speed. Derive the expression for it.

    Define escape velocity. Show that the escape velocity of a body from earth is independent on its mass.

    Derive an expression for the escape velocity of an object from the surface of earth. What is its value on the earth's surface ?

    Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

    Between the earth and the moon, which one has a greater escape velocity ? Give reason. or, Is the value of the escape velocity from the earth's surface the same as that from the surface of the moon ?

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