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A body weights 98 N on a spring balance ...

A body weights 98 N on a spring balance at the north pole. What will be its weight recorded on the same scale if it is shifted to te equator? Use g=`GM/R^2=9.8m/s^2` and the radius of the earth R=6400 km.

A

`99.66 N`

B

`110 N`

C

`97.66 N`

D

`106 N`

Text Solution

Verified by Experts

The correct Answer is:
A
Here `R = 6.4 xx 10^(3) km = 6.4 xx 10^(6) m`,
`g = 10 ms^(-2)`
At the pole, weight is same as the true weight
At weight `= mg`
`:. 100 N = m xx 10 m//s^(2)` or `m = 10 kg`
At the equator, latitude, `lambda = 0`, apparent weight is given by
`mg' = mg - mRomega^(2) cos^(2) lambda = mg - mR omega^(2) cos^(2) 0`
`mg' = mg - mRomega^(2)`
Also angular speed of an equatorial point on earth's surface is
`omega = (2pi)/(24 xx 60 xx 60) = 7.27 xx 10^(5) rad//s`
Now `mg' = 100 - 10 xx 6.4 xx 10^(6) (7.27 xx 10^(-5))^(2)`
`= 100 - 338.25 xx 10^(7) xx 10^(-10)`
`= 100 - 338.25 xx 10^(-3)`
`= 100 - 0.33825 ~~ 99.66 N`
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