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प्रश्न
Calculate the change in g value in your district of Tamil nadu. (Hint: Get the latitude of your district of Tamil nadu from Google). What is the difference in g values at Chennai and Kanyakumari?
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उत्तर
Variation of ‘g’ value in the latitude to Chennai
`"g’"_"Chennai" = "g" - ω^2"R" cos^2λ`
Here `ω^2"R" = ((2π)/"T")^2 xx "R"`
Period of revolution (T) = 1 day = 86400 sec
Radius of the Earth (R) = 6400 × 103 m
Latitude of Chennai (λ) = 13° = 0.2268 rad
`"g’"_"Chennai" = 9.8 - [((2 xx 3.14)/86400)^2 xx 6400 xx 10^3] xx (cos 0.2268)^2`
= `9.8 - [(3.4 xx 10^-2) xx (0.9744)^2]`
= 9.8 − [0.034 × 0.9494]
= 9.8 − 0.0323
`"g’"_"Chennai"` = 9.7677 ms−2
Variation of ‘g’ value in the latitude of Kanyakumari
`"λ’"_"Kanyakumari"` = 8°35’ = 0.1457 red
`"g’"_"Kanyakumari" = 9.8 - [3.4 xx 10^-2 xx (cos 0.1457)^2]`
= 9.8 − 0.0333
`"g’"_"Kanyakumari"` = 9.7667 ms−2
The difference of ‘g’ value Δg = `"g’"_"Chennai" - "g’"_"Kanyakumari"`
= 9.7677 − 9.7667
Δg = 0.001 ms−2
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