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Q.

A box weighs 196 N on a spring balance at the north pole. Its weight (in Newton) recorded on the same balance if it is shifted to the equator is_____ (Take $g = 10 m s^{- 2}$ at the north pole and the radius of the earth = 6400km)(Round off to the nearest integer)

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answer is 195.

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Detailed Solution

weight at equator = $m g^{'}$
$\begin{array}{l} = m (g - ω^{2} R) \\ mg = 196 N \Rightarrow m = 19.6 kg \\ \Rightarrow {mg}^{'} = 19.6 [10 - {(\frac{2 π}{24 \times 3600})}^{2} \times 6400 \times 10^{3}] N \\ = 19.6 [10 - 0.034] = 195.33 N \end{array}$

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