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A particle is taken to a distance r (gt ...

A particle is taken to a distance r (gt R) from centre of the earth. R is radius of the earth. It is given velocity V which is perpendicular to With the given values of V in column I you have to match the values of total energy of particle in column II and the resultant path of particle in column III. Here 'G' is the universal gravitational constant and 'M' is the mass of the earth.

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A, B, C, D
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Knowledge Check

  • A particle at a distance r from the centre of a uniform spherical planet of mass M radius R (ltr) has a velocity of magnitude v.

    A
    for `0 lt v lt sqrt((GM)/r` trajectory may be ellipse
    B
    for v `=sqrt((GM)/r` trajectory may be ellipse
    C
    for `sqrt((GM)/r lt v lt sqrt((2GM)/r` trajectory may be ellipse.
    D
    for v `=sqrt((GM)/r trajectory may be circle

  • The escape velocity of a sphere of mass m is given by (G=Universal gravitational constant,M=Mass of the earth and R_(e ) =Radius of the earth)

    A
    `sqrt((2GMm)/(R_(e ))`
    B
    `sqrt((2GM)/(R_(e ))`
    C
    `sqrt((GM)/(R_(e ))`
    D
    `sqrt((2GMm+R_(e ))/(R_(e ))`

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    A mass m is taken to a height R from the surface of the earth and then is given a vertical velocity upsilon . Find the minimum value of upsilon , so that mass never returns to the surface of the earth. (Radius of earth is R and mass of the earth m ).

    Match the constants given in column I with their values given in column II and mark the appropriate choice.

    Match the constants given in column I with their values given in column II and mark the appropriate choice.

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