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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

Text Solution

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`(T_(1))/(T_(2))=sqrt((g_(2))/(g_(1)))` but `g=(GM)/((R+h)^(2))`
`(g_(1))/(g_(2))=((R+h)/(R ))^(2)implies(T_(2))/(T_(1))=1+h//R`
`h=(T_(2)-T_(1))/(T_(1))xxR=(30xx6400)/(24xx3600)=2.2km`
`:.mu=2`
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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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    B
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    C
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    D
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    A
    gains 13.5 s/day
    B
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    C
    loses 108 s/day
    D
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