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A pendulum clock, which keeps correct ti...

A pendulum clock, which keeps correct time at sea level, loses `15s` per day when taken to the top of a mountain. If the radius of the earth is `6400km`, the height of the mountain is

A

`1.1km`

B

`2.2km`

C

`3.3km`

D

`4.4km`

Text Solution

Verified by Experts

The correct Answer is:
A
At height `h(h lt lt R_e)`
`g^'=g(1-(2h)/(R_e))`
`T^'/T=sqrt(g/g^')=sqrt((g)/(g(1-2h//R_e)))`
`=(1-(2h)/(R_e))^(-1//2)=1+h/R_e`
`(T^'/T-1)=h/R_e`
`(T^'/T-1)xx86400=h/R_exx86400`
`15=(h)/(6400)xx86400`
`h=1.1km`
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Knowledge Check

  • A pendulum clock which keeps correct time at the surface of the earth is taken into a mine, then

    A
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    C
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    A
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    B
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    gains 7 s

  • If a pendulum clock, keeps correct time at sea level is taken to a place 16 km below sea level, the clock will approximately

    A
    gains 13.5 s/day
    B
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    C
    loses 108 s/day
    D
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