Q: A box weighs 196 N on a spring balance at the north pole . Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 m/s^{2} at the north pole and radius of earth = 6400 km)

(a) 194.32 N

(b) 194.66 N

(c) 195.66 N

(d) 195.32 N

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Ans: (d)

Sol: Weight at north pole , mg = 196 N

At north pole , g = 10 m/s^{2}

R = 6400 km

$\large g_{equator} = g – \omega^2 R$

$\large m g_{equator} = m g – m \omega^2 R$

$\large = 196 – \frac{196}{10} \times \frac{6400 \times 10^3 \times 4 \pi^2}{(24 \times 60 \times 60)^2} $

= 195.32 N