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If a body is projected with speed v grea...

If a body is projected with speed `v` greater than escape speed `v_(e)` from the surface of earth, find its speed in intersteller space.

Text Solution

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Let `v` be the speed of projected body in interseller space, where gravitational force of earth is zero. Hence, the potential energy of the body is zero. Following the law of conservation of energy, we have
`1/2mv^(2)+((-GMm)/R)=1/2m(v')^(2)+0`
`(v')^(2)=v^(2)-(2GM)/R=v^(2)-v_(e)^(2)` (`:'=sqrt(2GM//R)`)
`v=sqrt(v^(2)-v_(e)^(2))`
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Knowledge Check

  • If a body is projected with a speed lesser than escape velocity, then

    A
    the body can reach a certain height and may fall down following a straight line path
    B
    the body can reach a certain height and may fall down following a parabolic path
    C
    the body may orbit the earth in a circular orbit
    D
    the body may orbit the earth in an elliptical orbit

  • The escape speed of a body from the surface of the Earth is

    A
    `2Rsqrt((2pi rho G)/(3))`
    B
    `2Rsqrt((pi rho G)/(3))`
    C
    `Rsqrt((2pi rho G)/(3))`
    D
    `sqrt((GM)/(R))`

  • If a body is thrown at speed of triple as that of escape speed (V_e) from earth s surface, then at what speed it will move in interstellar space?

    A
    `2sqrt2V_e`
    B
    `sqrt2V_e`
    C
    `V_e`
    D
    `sqrt3V_e`

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