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  4. A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use g =( GM / R 2)=9.8 ms -2 and radius of earth, R =6400 km .]

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Q. A body weighs $49\, N$ on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
(Use $g =\frac{ GM }{ R ^{2}}=9.8 ms ^{-2}$ and radius of earth, $R =6400 km .]$

JEE MainJEE Main 2021Gravitation

Solution:

Weight of pole $= mg =49 N$
At equator due to rotation $= g _{ e }= g - R \omega^{2}$
so $W = mg _{ e }= m \left( g - R \omega^{2}\right)$
$\therefore W _{ P } > W _{ e } \,\,\,\,W _{ P }=49 N$
So, $W _{ e }=48.83 N \,\,\,\,W _{ e } < 49 N$