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A particle of mass m is thrown upwards f...

A particle of mass m is thrown upwards from the surface of the earth with a velocity u the mass and the radius of the earth are respectively M and R .G is gravitational constant and g is acceleration due to gravity on the surface of the earth the minimum value of u so that the particle does not return back to earth is

A

`(sqrt(2GM)/(R)`

B

`(sqrt(2GM)/(R^2)`

C

`(sqrt(2GR^2))`

D

`(sqrt(R^2)/(2GM))`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Keeping the mass of the earth constant, if the radius of the earth is made 80% of its present value , the acceleration due to gravity on the earth's surface would

    A
    remain unchanged
    B
    decrease by 36% (approx.)
    C
    increase by 36% (approx.)
    D
    increase by 56% (approx.)

  • A ball of mass m is fired vertically upwards from the surface of the earth with velocity nv, where v_e is the escape velocity and n gt 1 . To what height will the ball rise? Neglecting air resistance, take radius of the earth as R

    A
    `R/n^2`
    B
    `R/(1-n^2)`
    C
    `(Rn^2)/(1-n^2)`
    D
    `Rn^2`

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