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A box weights $$196 N$$ 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 $$g = 10 ms^{-2}$$ at the north pole and the radius of the earth $$= 6400 km$$):

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Solution

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Weight of box measured at north pole $$\Rightarrow $$

$$w_p = 196 N = Mg , M = 19.6$$

Weight of box measured at equator,

$$w_e = w_p - w^2 R \times M$$

$$= 196 - (7.3 \times 10^{-5})^2 \times 6400 \times 10^3 \times M$$

$$[w = 7.3 \times 10^{-5}\, radius \, R = 6400 km]$$

$$= 196 - 53.29 \times 10^{-10} \times 6.4 \times 10^6 \times 19.6$$

$$= 196 - 0.0341 \times 19.6$$

$$w_e = 195.32 N$$

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