Question

# 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 $$= 6400 km$$):

A
$$195.66 N$$
B
$$194.32 N$$
C
$$195.32 N$$
D
$$194.66 N$$
Solution
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#### Correct option is C. $$195.32 N$$Weight of box measured at north pole $$\Rightarrow$$$$w_p = 196 N = Mg , M = 19.6$$Weight of box measured at equator,$$w_e = w_p - w^2 R \times M$$$$= 196 - (7.3 \times 10^{-5})^2 \times 6400 \times 10^3 \times M$$$$[w = 7.3 \times 10^{-5}\, radius \, R = 6400 km]$$$$= 196 - 53.29 \times 10^{-10} \times 6.4 \times 10^6 \times 19.6$$$$= 196 - 0.0341 \times 19.6$$$$w_e = 195.32 N$$

6
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