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Q.

A body weight 49 N is on spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
$[U s e g = \frac{G M}{R^{2}} = 9.8 m s^{- 2} a n d r a d i u s o f e a r t h, R = 6400 k m]$

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a

49 N

b

49.17 N

c

49.83 N

d

48.83 N

answer is D.

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Detailed Solution

$\begin{array}{l} A t p o l e, t h e r e i s n o e f f e c t o f r o t a t i o n o f e a r t h, \\ ∴ m g = 49 N \\ \Rightarrow m = \frac{49}{9.8} = 5 k g \\ A t e q u a t o r, A p p a r e n t W e i g h t = m (g - ω^{2} R) = 5 [9.8 - {(\frac{2 π}{24 \times 3600})}^{2} (6400 \times 10^{3})] = 48.83 N \end{array}$

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