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If radius of the earth contracts to half...

If radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?

Text Solution

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Present angular momentum of earth
`L_(1)=Iomega=(2)/(5)MR^(2)omega`
New angular momentum because of change in radius
`L_(2)=(2)/(5)M((R)/(2))^(2)omega'`
if external torque is zero then angular momentum
must be conserved
`L_(1)=L_(2)`
`(2)/(5)MR^(2)omega=(1)/(4)xx(2)/(5)MR^(2)omega'`
i.e., `omega'=4omega`
`T'=(1)/(4)T=(1)/(4)xx24=6h`
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Knowledge Check

  • If the earth were to suddenly contract to 1/nth of its present size without any change in its mass, the duration of the new day will be nearly

    A
    24/n hours
    B
    24 n hours
    C
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    D
    `24n^(2)` hours

  • If the earth were to suddenly contract to 1//n^(th) of its present radius without any change in its mass, the duration of the new day will be nearly

    A
    `24//n` hours
    B
    `24 n` hours
    C
    `24//n^(2)` hours
    D
    `24n^(2)` hours

  • If the earth were to suddenly contract to (1)/(n) th of its present radius without any change in its mass, the duration of the new day will be nearly

    A
    `(24)/(n)h`
    B
    24n b
    C
    `(24)/(n^(2))h`
    D
    `24n^(2)h`

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