Humanity uses energy at the rate of about `10^(13)` W. if we found a way to extract this energy from Eearth's rotation, approx how long would it take before the the day increased by 1 minute ? (Take mass of earth =`6xx10^(24) kg m R=6000 km, pi^(2)=10`)

Options

A. `10^(13)`
B. `10^(10) sec`
C. `10^(4) sec`
D. `10^(20) sec`

Answer

A

Explanation

`1/2 Iomega^(2)-10^(13) t=1/2 Iomega^(2)`
`1/2 xx2/5mR^(2)((4pi^(2))/(T^(2))-(4pi^(2))/((T+DeltaT)^(2)))`
`=10^(13)xxt`
`1/5xx6xx10^(24)xx(6xx10^(6))^(2)xx4pi^(2)((2T DeltaT)/(T^(4)))`
`=10^(13)t`
`481/5xx10^(24)xx6^(2)xx60/((24xx3600)^(3))=t`
`48/5xx10^(18)xx36xx60/(24^(2)xx24xx36xx36xx36)`
`(10^(19))/(108xx120xx24)~~10^(13)` sec