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Motion Under Gravity

Two equal mas...

Question

Two equal masses m and m are hung from a balance whose scale pans differ in vertical height by 'h'. The error in weighing in terms of density of the earth $ρ$ is :

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Solution

Variation of g with height
$g h = g (1 - \frac{2 h}{R})$
$\Rightarrow g - g h = \frac{2 g h}{R} 2. \frac{G M h}{R^{3}}$
$= \frac{2. G h}{R^{3}} . D . \frac{4 π}{3} R^{3}$
$∴ m g - m g h = \frac{8}{3} π G D m h$

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