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A particle of mass 'm' is raised to a he...

A particle of mass 'm' is raised to a height `h = R` from the surface of earth. Find increase in potential energy. `R =` radius of earth. `g =` acceleration due to gravity on the surface of earth.

Text Solution

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Gain in `P.E. =` infinal `P.E. -` initial `P.E.`
`= - (GM m)/((R + 3R)) - (-(GM m)/(R ))`
`= (3)/(4) (GM m)/(R ) = (3)/(4) mg R`
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Knowledge Check

  • An object is taken to height 2R above the surface of earth , the increase in potential energy is [ R is radius of earth ]

    A
    `(mgR)/2 `
    B
    `(mgR)/3 `
    C
    `(2mgR)/3`
    D
    2mgR

  • An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

    A
    `(gR^(2))/(R+h)`
    B
    `gR`
    C
    `(gR)/(R+h)`
    D
    `sqrt((gR^(2))/(R+h))`

  • If a body of mass m is raised to height 2 R from the earth s surface, then the change in potential energy of the body is (R is the radius of earth)

    A
    mgR
    B
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    C
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    D
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