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At what altitude will the acceleration d...

At what altitude will the acceleration due to gravity be `25%` of that at the earth's surface (given radius of earth is `R`)?

A

`R//4`

B

R

C

`3R//8`

D

`R//2`

Text Solution

Verified by Experts

The correct Answer is:
B
`g=(GM)/(r^(2)) rArr g_(0)=(GM)/(R^(2))` ..(i)
`g_(h)=(GM)/((R+h)^(2))` …..(ii)
`(g_(h))/(g_(0))=((R )/(R+h))^(2) rArr (1)/(4)=((R )/(R+h))^(2) rArr (R )/(R+h)=(1)/(2)`
`R+h =2R rArr h=R`
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Knowledge Check

  • The height vertically above the earth's surface at which the acceleration due to gravity becomes 1% of its value at the surface is (R is the radius of the earth)

    A
    8R
    B
    9R
    C
    10R
    D
    20R

  • The height at which the value of acceleration due to gravity becomes 50% of that at the surface of the earth. (radius of the earth = 6400 km ) is

    A
    `2630`
    B
    `2640`
    C
    `2650`
    D
    `2660`

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