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The earth is assumed to be a sphere of r...

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the earth. The value of f is

A

`1//2`

B

`sqrt(2)`

C

`1//sqrt(2)`

D

`1//3`.

Text Solution

Verified by Experts

The correct Answer is:
C
Escape velocity of the body from the surfaceof earth is `v=sqrt(2R)`
Escape velocity of the body from the platform is fv.
`:." potential energy "+" kinetic energy "=0`
`-(GMm)/(2R)+(1)/(2)mv^(2)=0 rArr v=sqrt((GM)/(R^(2))).R=sqrt(gR)=fv`
From the surface of the earth, `v_("escape")=sqrt(2gR)`
`:. fv=(v_("escape"))/(sqrt(2)) rArr f=(1)/(sqrt(2))`.
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Knowledge Check

  • The escape velocity from the surface of the Earth is

    A
    11.2km/s
    B
    11.2m/s
    C
    11.2 cm/s
    D
    11.2mm/s

  • The escape velocity of a body from the surface of earth is

    A
    11.2 km/s
    B
    11.4 km/s
    C
    11.6 km/s
    D
    11.0 km/s

  • The escape velocity from the surface of the earth does not depend on :

    A
    Mass of the earth
    B
    Mass of the body
    C
    radius of the earth
    D
    G

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