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How much below the surface of Earth does...

How much below the surface of Earth does the acceleration due to gravity become `70%` of its value on the surface of Earth. Radius of Earth `= 6.4 xx 10^(6) m`.

A

`0.6 xx 10^(7) m`

B

`1.92 xx 10^(6) m`

C

`1.1 xx 10^(4) m`

D

`8 xx 10^(4) m`

Text Solution

Verified by Experts

The correct Answer is:
B
Here `g'//g = 70// 100` and `d = ?`
Now `g' = g (1 - (d)/(R )), :. (g')/(g) = 1 - (d)/(R )`
or `(7)/(10 = 1 - (d)/(R )` or `(d)/(R ) = 1 - (7)/(10) = (3)/(10)`
or `d = (3R)/(10) = (3 xx 6.4 xx 10^(6))/(10) = 1.92 xx 10^(6) m`
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Knowledge Check

  • How much above the surface of earth does the accelration due to gravity reduces by 64% of its value on the earth. Radius of earth = 6400 km .

    A
    `5.71xx 10^(6)m`
    B
    `1.22 xx 10^(6)m`
    C
    `11 xx 10^(6)m`
    D
    `4.27 xx 10^(6)m`

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